Regularity and well-posedness of some quasi-linear elliptic and parabolic problems with nonlinear general Wentzell boundary conditions on nonsmooth domains

DOI10.1016/j.na.2012.05.004zbMath1253.35061OpenAlexW2043369547MaRDI QIDQ450596

Mahamadi Warma

Publication date: 13 September 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.05.004

zbMATH Keywords

weak solutions\(m\)-accretive operatorsHölder continuitynonlinear semigroupsquasi-linear elliptic equationsgeneral Wentzell boundary conditionsthe \(p\)-Laplace-Beltrami operator

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Smoothness and regularity of solutions to PDEs (35B65) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) A priori estimates in context of PDEs (35B45) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)

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Multivalued nonmonotone dynamic boundary condition ⋮ Generalized anisotropic elliptic Wentzell problems with nonstandard growth conditions ⋮ Semi-linear elliptic and elliptic-parabolic equations with Wentzell boundary conditions and \(L^1\)-data ⋮ Existence of bounded solutions for a class of quasilinear elliptic systems on manifolds with boundary ⋮ Approximation of a nonlinear fractal energy functional on varying Hilbert spaces ⋮ Variational approach to semilinear elliptic equation with nonlinear boundary ⋮ Quasi-linear variable exponent boundary value problems with Wentzell-Robin and Wentzell boundary conditions ⋮ Quasi-linear Venttsel' problems with nonlocal boundary conditions on fractal domains ⋮ Nonlinear parabolic flows with dynamic flux on the boundary ⋮ Ambrosetti-Prodi-type problems for quasi-linear elliptic equations with nonlocal boundary conditions ⋮ Nonautonomous semilinear Wentzell problems in fractal domains ⋮ Global regularity for a class of quasi-linear local and nonlocal elliptic equations on extension domains

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