Bruno Franchi

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All published works
Action Title Year Authors
+ Continuous primitives for higher degree differential forms in euclidean spaces, heisenberg groups and applications 2025 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ PDF Chat Primitives of volume forms in Carnot groups 2024 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ PDF Chat Homogenization of Smoluchowski-type equations with transmission boundary conditions 2024 Bruno Franchi
Silvia Lorenzani
+ PDF Chat Continuous primitives for higher degree differential forms in Euclidean spaces, Heisenberg groups and applications 2024 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ Homogenization of Smoluchowski-type equations with transmission boundary conditions 2024 Bruno Franchi
Silvia Lorenzani
+ PDF Chat On the heat kernel of the Rumin complex and Calderón reproducing formula 2024 Paolo Ciatti
Bruno Franchi
Yannick Sire
+ Cohomology of annuli, duality and L∞-differential forms on Heisenberg groups 2023 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ On the heat kernel of the Rumin complex and Calderón reproducing formula 2023 Paolo Ciatti
Bruno Franchi
Yannick Sire
+ PDF Chat Exceptional families of measures on Carnot groups 2023 Bruno Franchi
Irina Markina
+ Exceptional families of measures on Carnot groups 2022 Bruno Franchi
Irina Markina
+ The role of beta-amyloid and tau proteins in Alzheimer's disease: a mathematical model on graph 2022 Michiel Bertsch
Bruno Franchi
Maria Carla Tesi
Veronica Tora
+ Introduction to the Notes of the School on Analysis and Geometry in Metric Spaces 2021 Luigi Ambrosio
Bruno Franchi
Irina Markina
Francesco Serra Cassano
+ Cohomology of annuli, duality and $L^\infty$-differential forms on Heisenberg groups 2021 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ A sensitivity analysis of a mathematical model for the synergistic interplay of amyloid beta and tau on the dynamics of Alzheimer’s disease 2020 Michiel Bertsch
Bruno Franchi
Valentina Meschini
Maria Carla Tesi
Andrea Tosin
+ PDF Chat The amyloid cascade hypothesis and Alzheimer’s disease: A mathematical model 2020 Michiel Bertsch
Bruno Franchi
Luca Meacci
Mario Primicerio
Maria Carla Tesi
+ PDF Chat POINCARÉ AND SOBOLEV INEQUALITIES FOR DIFFERENTIAL FORMS IN HEISENBERG GROUPS AND CONTACT MANIFOLDS 2020 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ L1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups 2020 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ PDF Chat A mathematical model for Alzheimer’s disease: An approach via stochastic homogenization of the Smoluchowski equation 2020 Bruno Franchi
Martin Heida
Silvia Lorenzani
+ Orlicz spaces and endpoint Sobolev-Poincaré inequalities for differential forms in Heisenberg groups 2020 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ A Mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation 2019 Bruno Franchi
Martin Heida
Silvia Lorenzani
+ PDF Chat Gaffney–Friedrichs inequality for differential forms on Heisenberg groups 2019 Bruno Franchi
Francescopaolo Montefalcone
Elena Boet Serra
+ PDF Chat L1-Poincaré and Sobolev inequalities for differential forms in Euclidean spaces 2019 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ $L^1$-Poincar\'e and Sobolev inequalities for differential forms in Euclidean spaces 2019 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ $L^1$-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups 2019 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ A Mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation 2019 Bruno Franchi
Martin Heida
Silvia Lorenzani
+ $L^1$-Poincaré and Sobolev inequalities for differential forms in Euclidean spaces 2019 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ PDF Chat Well-Posedness of a Mathematical Model for Alzheimer's Disease 2018 Michiel Bertsch
Bruno Franchi
Maria Carla Tesi
Andrea Tosin
+ PDF Chat $$\Gamma $$ Γ -Convergence of variational functionals with boundary terms in Stein manifolds 2017 Eleonora Cinti
Bruno Franchi
María del Mar González
+ PDF Chat Microscopic and macroscopic models for the onset and progression of Alzheimer's disease 2017 Michiel Bertsch
Bruno Franchi
Maria Carla Tesi
Andrea Tosin
+ PDF Chat Smoluchowski Equation with Variable Coefficients in Perforated Domains: Homogenization and Applications to Mathematical Models in Medicine 2017 Bruno Franchi
Silvia Lorenzani
+ Poincar{é} and Sobolev inequalities for differential forms in Heisenberg groups 2017 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ $\Gamma$-convergence of variational functionals with boundary terms in Stein manifolds 2016 Eleonora Cinti
Bruno Franchi
María del Mar González
+ Alzheimer's disease: a mathematical model for onset and progression 2016 Michiel Bertsch
Bruno Franchi
Norina Marcello
Maria Carla Tesi
Andrea Tosin
+ PDF Chat From a Microscopic to a Macroscopic Model for Alzheimer Disease: Two-Scale Homogenization of the Smoluchowski Equation in Perforated Domains 2016 Bruno Franchi
Silvia Lorenzani
+ A recursive basis for primitive forms in symplectic spaces and applications to Heisenberg groups 2016 Annalisa Baldi
Marilena Barnabei
Bruno Franchi
+ $Γ$-convergence of variational functionals with boundary terms in Stein manifolds 2016 Eleonora Cinti
Bruno Franchi
María del Mar González
+ PDF Chat Gagliardo-Nirenberg inequalities for differential forms in Heisenberg groups 2015 Annalisa Baldi
Bruno Franchi
Pierre Pansu
+ PDF Chat Steiner’s formula in the Heisenberg group 2015 Zoltán M. Balogh
Fausto Ferrari
Bruno Franchi
Eugenio Vecchi
Kevin Wildrick
+ PDF Chat Intrinsic Lipschitz Graphs Within Carnot Groups 2015 Bruno Franchi
Raul Serapioni
+ PDF Chat Maxwell’s Equations in Anisotropic Media and Carnot Groups as Variational Limits 2015 Annalisa Baldi
Bruno Franchi
+ PDF Chat Area formula for centered Hausdorff measures in metric spaces 2015 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
+ Gagliardo-Nirenberg Inequalities for Horizontal Vector Fields in the Engel Group and in the Seven-Dimensional Quaternionic Heisenberg Group 2015 Annalisa Baldi
Bruno Franchi
Francesca Tripaldi
+ PDF Chat Harnack inequality for fractional sub-Laplacians in Carnot groups 2014 Fausto Ferrari
Bruno Franchi
+ Remarks on Lipschitz domains in Carnot groups 2014 Bruno Franchi
Valentina Penso
Raul Serapioni
+ PDF Chat Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem 2014 Bruno Franchi
Marco Marchi
Raul Serapioni
+ Sharp a priori estimates for div–curl systems in Heisenberg groups 2013 Annalisa Baldi
Bruno Franchi
+ On a class of semilinear evolution equations for vector potentials associated with Maxwell’s equations in Carnot groups 2013 Bruno Franchi
Enrico Obrecht
Eugenio Vecchi
+ A qualitative model for aggregation and diffusion of $$\beta $$ -amyloid in Alzheimer’s disease 2012 Yves Achdou
Bruno Franchi
Norina Marcello
Maria Carla Tesi
+ WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS 2012 Bruno Franchi
Maria Carla Tesi
+ Hessian inequalities and the fractional Laplacian 2011 Fausto Ferrari
Bruno Franchi
Igor E. Verbitsky
+ Differential forms in Carnot groups: a Γ-convergence approach 2011 Annalisa Baldi
Bruno Franchi
+ Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups 2010 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
+ Faraday’s Form and Maxwell’s Equations in the Heisenberg Group 2009 Bruno Franchi
Maria Carla Tesi
+ PDF Chat Compensated compactness for differential forms in Carnot groups and applications 2009 Annalisa Baldi
Bruno Franchi
Nicoletta Tchou
Maria Carla Tesi
+ PDF Chat Hypoellipticity, fundamental solution and Liouville type theorem for matrix-valued differential operators in Carnot groups 2009 Annalisa Baldi
Bruno Franchi
Maria Carla Tesi
+ Compensated compactness in the contact complex of Heisenberg groups 2008 Annalisa Baldi
Bruno Franchi
Maria Carla Tesi
+ Geometric Methods in PDE's: a conference on the occasion of the 65th birthday of Ermanno Lanconelli 2008 Giovanna Citti
Sever S Dragomir
Bruno Franchi
Cristian E. Gutiérrez
Annamaria Montanari
Andrea Pascucci
Sergio Polidoro
+ PDF Chat The Geometric Traveling Salesman Problem in the Heisenberg Group 2007 Fausto Ferrari
Bruno Franchi
Hervé Pajot
+ Convergence of a class of degenerate Ginzburg-Landau functionals and regularity for a subelliptic harmonic map equation 2006 Bruno Franchi
Elena Boet Serra
+ Heat Kernels, Stochastic Processes and Functional Inequalities 2006 Thierry Coulhon
Bruno Franchi
Takashi Kumagai
Karl‐Theodor Sturm
+ Regular submanifolds, graphs and area formula in Heisenberg groups 2006 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
+ Fundamental solution and sharp Lp estimates for Laplace operators in the contact complex of Heisenberg groups 2006 Annalisa Baldi
Bruno Franchi
Maria Carla Tesi
+ DIV–CURL TYPE THEOREM, H-CONVERGENCE AND STOKES FORMULA IN THE HEISENBERG GROUP 2006 Bruno Franchi
Nicoletta Tchou
Maria Carla Tesi
+ On a relative Alexandrov-Fenchel inequality for convex bodies in Euclidean spaces 2006 Fausto Ferrari
Bruno Franchi
Guozhen Lu
+ Courbure et sous-ensembles de courbes rectifiables dans le groupe de Heisenberg 2006 Fausto Ferrari
Bruno Franchi
Hervé Pajot
+ Homogenization and Convergence of Correctors in Carnot Groups 2005 Bruno Franchi
Cristian E. Gutiérrez
Truyen Nguyen
+ Mumford–Shah-type functionals associated with doubling metric measures 2005 Annalisa Baldi
Bruno Franchi
+ PDF Chat A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization 2004 Yves Achdou
Bruno Franchi
Nicoletta Tchou
+ On the structure of finite perimeter sets in step 2 Carnot groups 2003 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
+ A Sum Operator with Applications to Self-Improving Properties of Poincar� Inequalities in Metric Spaces 2003 Bruno Franchi
Carlos Pérez
Richard L. Wheeden
+ A $\Gamma$ -convergence result for doubling metric measures and associated perimeters 2003 Annalisa Baldi
Bruno Franchi
+ A Local Doubling Formula for the Harmonic Measure Associated with Subelliptic Operators and Applications† 2003 Fausto Ferrari
Bruno Franchi
+ PDF Chat Regular Hypersurfaces, Intrinsic Perimeter and Implicit Function Theorem in Carnot Groups 2003 Francesco Serra Cassano
Bruno Franchi
Raul Serapioni
+ $BV$ spaces and rectifiability for Carnot-Carathéodory metrics: an introduction 2003 Bruno Franchi
+ Two-scale homogenization in the Heisenberg group 2002 Bruno Franchi
Maria Carla Tesi
+ PDF Chat Rectifiability and perimeter in step 2 Groups 2002 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
+ Agmon metric for sum-of-squares operators 2001 Claudy Cancelier
Bruno Franchi
Elena Boet Serra
+ Rectifiability and perimeter in the Heisenberg group 2001 Raul Serapioni
Bruno Franchi
Francesco Serra Cassano
+ Sharp Geometric Poincaré Inequalities for Vector Fields and Non-Doubling Measures 2000 Bruno Franchi
Carlos Pérez
Richard L. Wheeden
+ PDF Chat How to get rid of one of the weights in a two-weight Poincaré inequality? 2000 Bruno Franchi
Piotr Hajłasz
+ Sur les ensembles de périmètre fini dans le groupe de heisenberg 1999 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
+ Some remarks about Poincaré type inequalities and representation formulas in metric spaces of homogeneous type 1999 Bruno Franchi
Richard L. Wheeden
+ PDF Chat Definitions of Sobolev classes on metric spaces 1999 Bruno Franchi
Piotr Hajłasz
Pekka Koskela
+ Some remarks about Poincaré type inequalities and representation formulas in metric spaces of homogeneous type 1999 Wheeden Richard L
Bruno Franchi
+ Self-Improving Properties of John–Nirenberg and Poincaré Inequalities on Spaces of Homogeneous Type 1998 Bruno Franchi
Carlos Pérez
Richard L. Wheeden
+ None 1998 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
+ PDF Chat Compensation couples and isoperimetric estimates for vector fields 1997 Bruno Franchi
Richard L. Wheeden
+ Subelliptic Estimates for a Class of Degenerate Elliptic Integro‐Differential Operators 1997 Claudy Cancelier
Bruno Franchi
+ Existence and Uniqueness of Nonnegative Solutions of Quasilinear Equations inRn 1996 Bruno Franchi
Ermanno Lanconelli
James Serrin
+ None 1996 Bruno Franchi
Guozhen Lu
Richard L. Wheeden
+ Gehring's lemma for metrics and higher integrability of the gradient for minimizers of noncoercive variational functionals 1996 Bruno Franchi
Francesco Serra Cassano
+ Weighted Poincar� inequalities for H�rmander vector fields and local regularity for a class of degenerate elliptic equations 1995 Bruno Franchi
G. Lu
Richard L. Wheeden
+ PDF Chat Representation formulas and weighted Poincaré inequalities for Hörmander vector fields 1995 Bruno Franchi
Guozhen Lu
Richard L. Wheeden
+ Weighted Poincaré Inequalities for Hörmander Vector Fields and local regularity for a class of degenerate elliptic equations 1995 Bruno Franchi
G. Lu
Richard L. Wheeden
+ Sobolev and isoperimetric inequalities for degenerate metrics 1994 Bruno Franchi
Sylvestre Gallot
Richard L. Wheeden
+ Weighted sobolev-poincaré inequalities for grushin type operators 1994 Bruno Franchi
Cristian E. Gutiérrez
Richard L. Wheeden
+ Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators 1994 Bruno Franchi
Cristian E. Gutiérrez
Richard L. Wheeden
+ Nontrivial solutions for Monge-Ampère type operators in convex domains 1993 Bruno Franchi
N. D. Kutev
Sergio Polidoro
+ Global Solutions for a Class of Monge-Ampère Equations 1992 Bruno Franchi
+ Weighted Sobolev-Poincare Inequalities and Pointwise Estimates for a Class of Degenerate Elliptic Equations 1991 Bruno Franchi
+ PDF Chat Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations 1991 Bruno Franchi
+ Existence and Uniqueness of Ground State Solutions of Quasilinear Elliptic Equations 1988 Bruno Franchi
Ermanno Lanconelli
James Serrin
+ Radial Symmetry of the Ground States for a Class of Quasilinear Elliptic Equations 1988 Bruno Franchi
Ermanno Lanconelli
+ Pointwise estimates for a class of strongly degenerate elliptic operators : a geometrical approach 1987 Bruno Franchi
Raul Serapioni
+ Trace Theorems for Anisotropic Weighted SOBOLEV Spaces in a Corner 1986 Bruno Franchi
+ An embedding theorem for sobolev spaces related to non-smooth vector fieldsand harnack inequality 1984 Bruno Franchi
Ermanno Lanconelli
+ Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients 1983 Bruno Franchi
Ermanno Lanconelli
Common Coauthors
Commonly Cited References
Action Title Year Authors # of times referenced
+ Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals 2002 Elias M. Stein
Timothy S Murphy
26
+ PDF Chat Subelliptic estimates and function spaces on nilpotent Lie groups 1975 Gerald B. Folland
26
+ Hardy spaces on homogeneous groups 1982 Gerald B. Folland
Elias M. Stein
24
+ Geometric Measure Theory 1988 Herbert Fédérer
24
+ On the structure of finite perimeter sets in step 2 Carnot groups 2003 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
19
+ Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces 1996 Nicola Garofalo
Duy-Minh Nhieu
19
+ The Poincaré inequality for vector fields satisfying Hörmander’s condition 1986 David Jerison
19
+ PDF Chat Balls and metrics defined by vector fields I: Basic properties 1985 Alexander Nagel
Elias M. Stein
Stephen Wainger
18
+ Regular submanifolds, graphs and area formula in Heisenberg groups 2006 Bruno Franchi
Raul Serapioni
Francesco Serra Cassano
18
+ Stratified Lie Groups and Potential Theory for their Sub-Laplacians 2007 Andrea Bonfiglioli
Ermanno Lanconelli
Francesco Uguzzoni
18
+ Analysis and Geometry on Groups 1993 N. Th. Varopoulos
Laurent Saloff‐Coste
Thierry Coulhon
18
+ PDF Chat Formes différentielles sur les variétés de contact 1994 Michel Rumin
17
+ Rectifiability and perimeter in the Heisenberg group 2001 Raul Serapioni
Bruno Franchi
Francesco Serra Cassano
16
+ PDF Chat Compensated compactness for differential forms in Carnot groups and applications 2009 Annalisa Baldi
Bruno Franchi
Nicoletta Tchou
Maria Carla Tesi
16
+ Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients 1983 Bruno Franchi
Ermanno Lanconelli
15
+ PDF Chat Around heat decay on forms and relations of nilpotent Lie groups 2001 Michel Rumin
14
+ Sobolev and isoperimetric inequalities for degenerate metrics 1994 Bruno Franchi
Sylvestre Gallot
Richard L. Wheeden
14
+ Weighted sobolev-poincaré inequalities for grushin type operators 1994 Bruno Franchi
Cristian E. Gutiérrez
Richard L. Wheeden
14
+ PDF Chat Representation formulas and weighted Poincaré inequalities for Hörmander vector fields 1995 Bruno Franchi
Guozhen Lu
Richard L. Wheeden
14
+ PDF Chat The geometric Sobolev embedding for vector fields and the isoperimetric inequality 1994 Luca Capogna
Donatella Danielli
Nicola Garofalo
13
+ PDF Chat On the nonexistence of bilipschitz parameterizations and geometric problems about $A_\infty$-weights 1996 Stephen Semmes
13
+ Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie groups 1999 Michel Rumin
13
+ Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un 1989 Pierre Pansu
13
+ PDF Chat Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications 1992 Guozhen Lu
12
+ Weighted Inequalities for Fractional Integrals on Euclidean and Homogeneous Spaces 1992 Eric T. Sawyer
Richard L. Wheeden
12
+ PDF Chat Hypoellipticity, fundamental solution and Liouville type theorem for matrix-valued differential operators in Carnot groups 2009 Annalisa Baldi
Bruno Franchi
Maria Carla Tesi
12
+ PDF Chat Regular Hypersurfaces, Intrinsic Perimeter and Implicit Function Theorem in Carnot Groups 2003 Francesco Serra Cassano
Bruno Franchi
Raul Serapioni
12
+ PDF Chat Carnot-Carathéodory spaces seen from within 1996 Mikhael Gromov
12
+ Geometry of Sets and Measures in Euclidean Spaces 1995 Pertti Mattila
12
+ PDF Chat Hypoelliptic differential operators and nilpotent groups 1976 Linda Preiss Rothschild
E. M. Stein
12
+ PDF Chat Hypoelliptic second order differential equations 1967 Lars Hörmander
11
+ Geometric Measure Theory 1996 Herbert Fédérer
11
+ WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS 2012 Bruno Franchi
Maria Carla Tesi
11
+ PDF Chat Inequalities for the maximal function relative to a metric 1976 A. Calderón
11
+ PDF Chat Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations 1991 Bruno Franchi
11
+ Compensated compactness in the contact complex of Heisenberg groups 2008 Annalisa Baldi
Bruno Franchi
Maria Carla Tesi
11
+ A Tour of Subriemannian Geometries, Their Geodesics and Applications 2006 Richard Montgomery
10
+ Measure Theory and Fine Properties of Functions 2018 Lawrence C. Evans
Ronald F. Garzepy
10
+ PDF Chat Elliptic Partial Differential Equations of Second Order 2001 David Gilbarg
Neil S. Trudinger
9
+ PDF Chat New estimates for elliptic equations and Hodge type systems 2007 Jean Bourgain
Haı̈m Brezis
9
+ DIV–CURL TYPE THEOREM, H-CONVERGENCE AND STOKES FORMULA IN THE HEISENBERG GROUP 2006 Bruno Franchi
Nicoletta Tchou
Maria Carla Tesi
9
+ PDF Chat The sharp Poincaré inequality for free vector fields: an endpoint result 1994 Guozhen Lu
9
+ Sub-Riemannian limit of the differential form spectrum of contact manifolds 2000 Michel Rumin
9
+ Rectifiable sets in metric and Banach spaces 2000 Luigi Ambrosio
Bernd Kirchheim
9
+ A qualitative model for aggregation and diffusion of $$\beta $$ -amyloid in Alzheimer’s disease 2012 Yves Achdou
Bruno Franchi
Norina Marcello
Maria Carla Tesi
9
+ A recursive basis for primitive forms in symplectic spaces and applications to Heisenberg groups 2016 Annalisa Baldi
Marilena Barnabei
Bruno Franchi
9
+ PDF Chat Existence of solutions for the discrete coagulation-fragmentation model with diffusion 1997 Dariusz Wrzosek
8
+ PDF Chat Currents in metric spaces 2000 Luigi Ambrosio
Bernd Kirchheim
8
+ PDF Chat From a Microscopic to a Macroscopic Model for Alzheimer Disease: Two-Scale Homogenization of the Smoluchowski Equation in Perforated Domains 2016 Bruno Franchi
Silvia Lorenzani
8
+ PDF Chat A note on div curl inequalities 2005 Loredana Lanzani
E. M. Stein
8