Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients

DOI10.1090/memo/1311zbMath1494.35001OpenAlexW3135305743MaRDI QIDQ4983689

Ruipeng Shen, Cristian Rios, Lyudmila Korobenko, Eric T. Sawyer

Publication date: 26 April 2021

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/1311

zbMATH Keywords

regularityquasilinear equationsrough coefficientsOrlicz-Sobolev inequalityinfinite degeneracynon-doubling control ballssubrepresentation inequality

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Maximum principles in context of PDEs (35B50) Degenerate elliptic equations (35J70) Metric geometry (51F99) Weak solutions to PDEs (35D30) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Close-to-elliptic equations (35H99)

Related Items (6)

Weighted 1-dimensional Orlicz-Poincaré inequalities ⋮ Matrix weights and regularity for degenerate elliptic equations ⋮ Continuity of infinitely degenerate weak solutions via the trace method ⋮ Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators ⋮ Orlicz-Sobolev inequalities and the doubling condition ⋮ Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients

Cites Work

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• Hypoellipticity for infinitely degenerate quasilinear equations and the Dirichlet problem
• A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations
• A priori estimates for infinitely degenerate quasilinear equations.
• Une condition géométrique pour l'inégalité de Harnack. (A geometric condition for Harnack's inequality)
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Non-hypoellipticity for degenerate elliptic operators
• The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics
• A priori estimates for quasilinear equations related to the Monge-Ampère equation in two dimensions
• Regularity of degenerate Monge-Ampère and prescribed Gaussian curvature equations in two dimensions
• Hypoelliptic second order differential equations
• Degenerate Sobolev spaces and regularity of subelliptic equations
• An embedding theorem for sobolev spaces related to non-smooth vector fieldsand harnack inequality
• Weighted Sobolev-Poincare Inequalities and Pointwise Estimates for a Class of Degenerate Elliptic Equations
• Elliptic Partial Differential Equations of Second Order
• Nonanalytic-hypoellipticity for some degenerate elliptic operators
• Maximum Principle, Nonhomogeneous Harnack Inequality, and Liouville Theorems forX-Elliptic Operators
• Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients
• From Sobolev inequality to doubling
• Hölder continuity of weak solutions to subelliptic equations with rough coefficients
• On a pointwise estimate for parabolic differential equations
• ON A CRITERION FOR HYPOELLIPTICITY

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