Boundary value problems of elliptic and parabolic type with boundary data of negative regularity

Felix Hummel

Type: Article

Publication Date: 2021-01-18

Citations: 7

DOI: https://doi.org/10.1007/s00028-020-00664-0

Abstract

We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the singularities of solutions at the boundary. To this end, we derive mapping properties of Poisson operators in mixed scales with mixed smoothness. We also derive $\mathcal{R}$-sectoriality results for homogeneous boundary data in the case that the smoothness in normal direction is not too large.

Locations

arXiv (Cornell University) - View - PDF
DataCite API - View
Journal of Evolution Equations - View - PDF

Similar Works

Action	Title	Year	Authors
+	Hölder Regularity for Domains of Fractional Powers of Elliptic Operators with Mixed Boundary Conditions	2022	Robert Haller Hannes Meinlschmidt Joachim Rehberg
+ PDF Chat	Elliptic and parabolic regularity for second‐ order divergence operators with mixed boundary conditions	2015	Robert Haller‐Dintelmann Alf Jonsson Dorothee Knees Joachim Rehberg
+	Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces	2019	Felix Hummel Nick Lindemulder
+	Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces	2019	Felix Hummel Nick Lindemulder
+	Uniform Shapiro-Lopatinski Conditions and Boundary Value Problems on Manifolds with Bounded Geometry	2019	Nadine Große Victor Nistor
+	Maximal parabolic regularity for divergence operators including mixed boundary conditions	2009	Robert Haller‐Dintelmann Joachim Rehberg
+	On elliptic and parabolic regularity for mixed boundary value problems	2012	Robert Haller‐Dintelmann Alf Jonsson Dorothee Knees Joachim Rehberg
+	Regularity theory for parabolic operators in the half-space with boundary degeneracy	2023	Giorgio Metafune Luigi Negro Chiara Spina
+	Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values	2021	Cornelia Schneider Flóra Orsolya Szemenyei
+ PDF Chat	Boundary regularity for a degenerate elliptic equation with mixed boundary conditions	2018	Alassane Niang
+	Elliptic problems with rough boundary data in generalized Sobolev spaces	2020	Anna Anop Robert Denk Aleksandr Murach
+	Elliptic problems with rough boundary data in generalized Sobolev spaces	2020	Anna Anop Robert Denk Aleksandr Murach
+ PDF Chat	Boundary value problems with mixed lateral conditions for parabolic operators	1982	Antonio Bove Bruno Franchi Enrico Obrecht
+	The Neumann Green function and scale invariant regularity estimates for elliptic equations with Neumann data in Lipschitz domains	2023	Seick Kim Georgios Sakellaris
+ PDF Chat	Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values	2022	Cornelia Schneider Flóra Orsolya Szemenyei
+	Besov regularity for operator equations on patchwise smooth manifolds	2013	Stephan Dahlke Markus Weimar
+	Besov regularity for operator equations on patchwise smooth manifolds	2013	Stephan Dahlke Markus Weimar
+ PDF Chat	Maximal parabolic regularity for divergence operators including mixed boundary conditions	2009	Robert Haller‐Dintelmann Joachim Rehberg
+	Hölder estimates for parabolic operators on domains with rough boundary	2015	Karoline Disser A. F. M. ter Elst Joachim Rehberg
+ PDF Chat	Elliptic operators and boundary problems in spaces of generalized smoothness	2024	Vladimir Mikhailets Aleksandr Murach Iryna Chepurukhina

Works That Cite This (7)

Action	Title	Year	Authors
+	Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces	2019	Felix Hummel Nick Lindemulder
+ PDF Chat	Some problems for Petrovskii parabolic systems in generalized Sobolev spaces	2022	Oleksandr Diachenko Valerii Los
+ PDF Chat	Еліптичні задачі з грубими крайовими даними у просторах Нікольського	2021	Aleksandr Murach Iryna Chepurukhina
+	Elliptic problems with rough boundary data in Nikolskii spaces	2021	Aleksandr Murach Iryna Chepurukhina
+	Elliptic problems in Besov and Sobolev-Triebel-Lizorkin spaces of low regularity	2021	Iryna Chepurukhina Aleksandr Murach
+ PDF Chat	Sample paths of white noise in spaces with dominating mixed smoothness	2021	Felix Hummel
+	Sample Paths of White Noise in Spaces with Dominating Mixed Smoothness	2020	Felix Hummel

Works Cited by This (52)

Action	Title	Year	Authors
+	Heat kernels and maximal l<sup>p</sup>—l<sup>q</sup>estimates for parabolic evolution equations	1997	Matthias Hieber Pruss Jan
+	Semigroups of Linear Operators and Applications to Partial Differential Equations	1983	A. Pazy
+	Classical Fourier Analysis	2014	Loukas Grafakos
+ PDF Chat	Perturbation, interpolation, and maximal regularity	2006	Bernhard H. Haak Markus Haase Peer Christian Kunstmann
+	Theory of function spaces	1983	Hans Triebel
+	Non-Homogeneous Boundary Value Problems and Applications	1973	J. L. Lions Enrico Magenes
+	$H^\infty $ functional calculus for an elliptic operator on a half-space with general boundary conditions	2002	Giovanni Dore Alberto Venni
+	Lectures on the H-Cobordism Theorem	1965	John Milnor
+ PDF Chat	Stochastic partial differential equations with Dirichlet white-noise boundary conditions	2002	Elisa Alòs Stefano Bonaccorsi
+	Pseudodifferential operators on Bochner spaces and an application	2006	Pierre Portal Željko Štrkalj