Global Regularity of Weak Solutions to Quasilinear Elliptic and Parabolic Equations with Controlled Growth

DOI10.1080/03605302.2011.571746zbMath1233.35059arXiv1005.5208OpenAlexW1990071083MaRDI QIDQ3106545

Hongjie Dong, Do-Yoon Kim

Publication date: 28 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.5208

zbMATH Keywords

boundary value problemsLipschitz domainsdivergence form equationsBMO coefficients

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Weak solutions to PDEs (35D30) Quasilinear elliptic equations (35J62) Quasilinear parabolic equations (35K59)

Related Items (20)

Regularity of solutions of the model Venttsel' problem for quasilinear parabolic systems with nonsmooth in time principal matrices ⋮ Weighted Lorentz estimates for nonlinear elliptic obstacle problems with partially regular nonlinearities ⋮ Regularity estimates for BMO-weak solutions of quasilinear elliptic equations with inhomogeneous boundary conditions ⋮ \(L^{p}\)-estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth ⋮ Morrey regularity for nonlinear elliptic equations with partial BMO nonlinearities under controlled growth ⋮ Morrey regularity of solutions to quasilinear elliptic equations over Reifenberg flat domains ⋮ Partial regularity for solutions of quasilinear parabolic systems with nonsmooth in time principal matrix ⋮ \(L^p\) estimates for weak solutions to nonlinear degenerate parabolic systems ⋮ On critical \(p\)-Laplacian systems ⋮ Boundedness of the solutions to non-linear systems with Morrey data ⋮ Regularity problem for \(2m\)-order quasilinear parabolic systems with non smooth in time principal matrix. \((A(t),m)\)-caloric approximation method ⋮ Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities ⋮ Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials ⋮ Hölder regularity for weak solutions to divergence form degenerate quasilinear parabolic systems ⋮ Two-phase problem for quasilinear parabolic systems with nondiagonal principal matrix. Regularity of weak solutions ⋮ Regularity of weak solutions to the model Venttsel problem for linear parabolic systems with nonsmooth in time principal matrix: \(A(t)\)-caloric approximation method ⋮ Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices ⋮ Interior gradient estimates for weak solutions of quasilinear \(p\)-Laplacian type equations ⋮ Lorentz Estimates for Weak Solutions of Quasi-linear Parabolic Equations with Singular Divergence-free Drifts ⋮ Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients

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