Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane

Kari Astala, Tadeusz Iwaniec, Gaven Martin

Type: Article

Publication Date: 2006-01-24

Citations: 19

DOI: https://doi.org/10.1515/crelle.2006.014

View Publication

Locations

Journal für die reine und angewandte Mathematik (Crelles Journal) - View

Similar Works

Action	Title	Year	Authors
+	Corrigendum to “Aleksandrov–Bakelman–Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE” [J. Differential Equations 264 (2018) 2708–2736]	2018	Chenchen Mou Andrzej Święch
+ PDF Chat	Book Review: Maximum principles and sharp constants for solutions of elliptic and parabolic systems	2014	Dmitry Khavinson
+	The maximum principle for degenerate parabolic PDEs with singularities	1994	Hitoshi Ishii
+	The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients	2020	Boyan Sirakov Philippe Souplet
+	The V\'azquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients	2020	Boyan Sirakov Philippe Souplet
+	An Intrinsic Harnack inequality for some non-homonegeneous parabolic equations in non-divergence form	2021	Vedansh Arya
+	Continuity of infinitely degenerate weak solutions via the trace method	2020	Lyudmila Korobenko Eric T. Sawyer
+ PDF Chat	Concavity of solutions to degenerate elliptic equations on the sphere	2020	Mat Langford Julian Scheuer
+	On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems	2019	Sajan K. Samuel
+ PDF Chat	Convex integration and the Lp theory of elliptic equations	2009	Kari Astala Daniel Faraco László Székelyhidi
+	Inhomogeneous Hopf–Oleĭnik Lemma and regularity of semiconvex supersolutions via new barriers for the Pucci extremal operators	2018	J. Ederson M. Braga Diego Moreira
+	Continuity of infinitely degenerate weak solutions via the trace method	2020	Lyudmila Korobenko Eric T. Sawyer
+	Harnack Inequality and Fundamental Solution for Degenerate Hypoelliptic Operators	2017	Erika Battaglia
+ PDF Chat	The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients	2021	Boyan Sirakov Philippe Souplet
+ PDF Chat	A Sharp Maximum Principle for Degenerate Elliptic-Parabolic Equations	1970	C. Denson Hill
+ PDF Chat	Explicit subsolutions and a Liouville theorem for fully nonlinear uniformly elliptic inequalities in halfspaces	2012	Fabiana Leoni
+	Uniqueness of the critical point for solutions to some $p$-Laplace equations in the plane	2022	William Borrelli Sunra Mosconi Marco Squassina
+	Convex hull property for elliptic and parabolic systems of PDE	2023	Antonín Češík
+ PDF Chat	Uniqueness of the critical point for solutions of some p-Laplace equations in the plane	2023	William Borrelli Sunra Mosconi Marco Squassina
+	Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions	2008	Xavier Cabré

Works That Cite This (19)

Action	Title	Year	Authors
+	The normal derivative lemma and surrounding issues	2022	D. E. Apushkinskaya Alexander I. Nazarov
+	Weighted estimates for Beltrami equations	2013	Albert Clop Victor Cruz
+ PDF Chat	The Dirichlet Problem for elliptic equations in unbounded domains of the plane	2008	Paola Cavaliere Maria Transirico
+ PDF Chat	A W<sup>2,p</sup>-ESTIMATE FOR A CLASS OF ELLIPTIC OPERATORS	2013	Sara Monsurrò Maria Transirico
+	The Precise Lp-theory of Elliptic Equations in the Plane	2005	Carlo Sbordone
+ PDF Chat	Convex integration and the Lp theory of elliptic equations	2009	Kari Astala Daniel Faraco László Székelyhidi
+ PDF Chat	On Hölder regularity for elliptic equations of non-divergence type in the plane	2009	Albert Baernstein Leonid V. Kovalev
+ PDF Chat	On quasiconvex hulls in symmetric $ 2\times2 $ matrices	2006	László Székelyhidi
+ PDF Chat	ELLIPTIC EQUATIONS WITH COMPACTLY SUPPORTED SOLUTIONS	2013	Orazio Arena Cristina Giannotti
+ PDF Chat	On reduced Beltrami equations and linear families of quasiregular mappings	2012	Jarmo Jääskeläinen

Works Cited by This (21)

Action	Title	Year	Authors
+	Fully Nonlinear Elliptic Equations	1995	Luis Caffarelli Xavier Cabré
+	Geometric Function Theory and Non-linear Analysis	2001	Tadeusz Iwaniec Gaven Martin
+ PDF Chat	Convex integration and the Lp theory of elliptic equations	2009	Kari Astala Daniel Faraco László Székelyhidi
+ PDF Chat	Elliptic Partial Differential Equations of Second Order	2001	David Gilbarg Neil S. Trudinger
+	On the alexandroff‐bakelman‐pucci estimate and the reversed hölder inequality for solutions of elliptic and parabolic equations	1995	Xavier Cabré
+	Operatori ellittici estremanti	1966	Carlo Pucci
+ PDF Chat	A surprising higher integrability property of mappings with positive determinant	1989	Stefan Müller
+	Mappings of finite distortion: Monotonicity and continuity	2001	Tadeusz Iwaniec Pekka Koskela Jani Onninen
+ PDF Chat	On mappings with integrable dilatation	1993	Tadeusz Iwaniec Vladimír Šverák
+ PDF Chat	Limitazioni per soluzioni di equazioni ellittiche	1966	Carlo Pucci