Finite energy solutions to inhomogeneous nonlinear elliptic equations with sub-natural growth terms

DOI10.1515/acv-2017-0035zbMath1436.35207arXiv1709.02048OpenAlexW3105862262MaRDI QIDQ2285854

Igor E. Verbitsky, Adisak Seesanea

Publication date: 9 January 2020

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02048

zbMATH Keywords

quasilinear elliptic equation\(p\)-Laplacianfractional LaplacianWolff potentialfinite energy solution

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (9)

Solutions to sublinear elliptic equations with finite generalized energy ⋮ Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms ⋮ Bilateral estimates of solutions to quasilinear elliptic equations with sub-natural growth terms ⋮ Solutions in Lebesgue spaces to nonlinear elliptic equations with subnatural growth terms ⋮ Global pointwise estimates of positive solutions to sublinear equations ⋮ Uniqueness of entire solutions to quasilinear equations of \(p \)-Laplace type ⋮ Minimal \(L^p\)-solutions to singular sublinear elliptic problems ⋮ The Dirichlet problem for sublinear elliptic equations with source ⋮ Wolff's inequality for intrinsic nonlinear potentials and quasilinear elliptic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear elliptic equations and intrinsic potentials of Wolff type
• On the Picard principle for \(\Delta + \mu \)
• Convexity properties of Dirichlet integrals and Picone-type inequalities
• Superharmonic functions are locally renormalized solutions
• Sublinear elliptic equations in \(\mathbb{R}{}^ n\)
• The Wiener test and potential estimates for quasilinear elliptic equations
• A sublinear version of Schur's lemma and elliptic PDE
• Thin sets in nonlinear potential theory
• Finite energy solutions of quasilinear elliptic equations with sub-natural growth terms
• Quasilinear and Hessian equations of Lane-Emden type
• Global estimates for kernels of Neumann series and Green's functions
• Weighted Norm Inequalities of (1, q)-Type for Integral and Fractional Maximal Operators
• ON $L^p$–$L^q$ TRACE INEQUALITIES
• A property of sobolev spaces
• Trace Inequalities of Sobolev Type in the Upper Triangle Case
• On the weak continuity of elliptic operators and applications to potential theory
• Some results and examples about the behavior of harmonic functions and Green’s functions with respect to second order elliptic operators
• Positive Solutions to Schrödinger’s Equation and the Exponential Integrability of the Balayage
• Guide to nonlinear potential estimates
• Sobolev Spaces

This page was built for publication: Finite energy solutions to inhomogeneous nonlinear elliptic equations with sub-natural growth terms