Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators

zbMath1496.35020arXiv2008.08263MaRDI QIDQ5101479

Lyudmila Korobenko, Usman Hafeez, Lucas Williams, Théo Lavier

Publication date: 30 August 2022

Full work available at URL: https://arxiv.org/abs/2008.08263

zbMATH Keywords

Dirichlet problemsolvabilityglobal boundednessrough coefficientsOrlicz-Sobolev inequalityinfinite degeneracy

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70) Weak solutions to PDEs (35D30) Subelliptic equations (35H20) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

• Continuity of Solutions of Parabolic and Elliptic Equations
• On Harnack's theorem for elliptic differential equations
• The local regularity of solutions of degenerate elliptic equations
• 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
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