Regularity theory in Orlicz spaces for elliptic equations in Reifenberg domains

DOI10.1016/j.jmaa.2006.12.081zbMath1178.35154OpenAlexW2074227340MaRDI QIDQ996865

Huilian Jia, Dongsheng Li, Lihe Wang

Publication date: 19 July 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.12.081

zbMATH Keywords

compactness methodmaximal functionReifenberg flat domainVitali covering lemma

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25)

Related Items (14)

Uniform estimates with data from generalized Lebesgue spaces in periodic structures ⋮ An end point Orlicz type estimate for nonlinear elliptic equations ⋮ Gradient estimates for nonlinear elliptic equations with vanishing Neumann data in quasiconvex domains ⋮ Global gradient estimates for Dirichlet problems of elliptic operators with a BMO antisymmetric part ⋮ Sharp conditions for Korn inequalities in Orlicz spaces ⋮ Gradient estimates for higher order elliptic equations on nonsmooth domains ⋮ Stationary flows of shear thickening fluids in 2D ⋮ Global regularity for divergence form elliptic equations in Orlicz spaces on quasiconvex domains ⋮ Analysis of generalized Navier-Stokes equations for stationary shear thickening flows ⋮ Generalizations of Korn's inequality based on gradient estimates in Orlicz spaces and applications to variational problems in 2D involving the trace free part of the symmetric gradient ⋮ Gradient estimates in Orlicz space for nonlinear elliptic equations ⋮ Gradient weighted norm inequalities for linear elliptic equations with discontinuous coefficients ⋮ Weighted gradient estimates for elliptic problems with Neumann boundary conditions in Lipschitz and (semi-)convex domains ⋮ Regularity in Orlicz spaces for nondivergence degenerate elliptic equations in Carnot groups

Cites Work

• Traces of Sobolev functions on fractal type sets and characterization of extension domains
• A geometric approach to the Calderón-Zygmund estimates
• Reifenberg flat metric spaces, snowballs, and embeddings
• On the regularity of solutions to the Poisson equation in Orlicz-spaces
• Elliptic equations with BMO coefficients in Reifenberg domains
• An existence theorem for a strongly nonlinear elliptic problem in Orlicz spaces
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