Existence of weak solutions to degenerate \(p\)-Laplacian equations and integral formulas

DOI10.1016/j.jde.2017.08.039zbMath1380.35112OpenAlexW2767184168MaRDI QIDQ2411365

Seng-Kee Chua, Richard L. Wheeden

Publication date: 20 October 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2017.08.039

zbMATH Keywords

degenerate Sobolev spacesdegenerate \(p\)-Laplacian

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items

Boundedness and regularity of solutions of degenerate elliptic partial differential equations ⋮ Bounded weak solutions to elliptic PDE with data in Orlicz spaces ⋮ Embedding and compact embedding for weighted and abstract Sobolev spaces

Cites Work

• A compact embedding theorem for generalized Sobolev spaces
• Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients.
• Harnack's inequality and Hölder continuity for weak solutions of degenerate quasilinear equations with rough coefficients
• Degenerate elliptic inequalities with critical growth
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Sub-Riemannian geometry
• Mountain pass solutions to equations of \(p\)-Laplacian type.
• Lectures on analysis on metric spaces
• A concentration-compactness lemma with applications to singular eigenvalue problems
• Representation formulas and weighted Poincaré inequalities for Hörmander vector fields
• Boundedness and regularity of solutions of degenerate elliptic partial differential equations
• Dual variational methods in critical point theory and applications
• Existence and spectral theory for weak solutions of Neumann and Dirichlet problems for linear degenerate elliptic operators with rough coefficients
• Existence results for Brezis-Nirenberg problems with Hardy potential and singular coefficients
• The solvability of quasilinear Brezis-Nirenberg-type problems with singular weights
• Hypoelliptic second order differential equations
• Hardy—Poincaré inequalities with boundary singularities
• On singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent
• Existence of Weak Solutions of Linear Subelliptic Dirichlet Problems with Rough Coefficients
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Degenerate Sobolev spaces and regularity of subelliptic equations
• Weighted Poincare and Sobolev Inequalities and Estimates for Weighted Peano Maximal Functions
• The local regularity of solutions of degenerate elliptic equations
• Sobolev met Poincaré
• On the Existence of Positive Solutions of Semilinear Elliptic Equations
• Hölder continuity of weak solutions to subelliptic equations with rough coefficients
• Variational Methods
• Extension Theorems on Weighted Sobolev Spaces and Some Applications
• Measure and integration theory. Transl. from the German by Robert B. Burckel
• Variational and topological methods for Dirichlet problems with \(p\)-Laplacian
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