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- W4300546647 abstract "We prove Holder continuity up to the boundary for solutions of quasi-linear degenerate elliptic problems in divergence form, not necessarily of variational type, on Lipschitz domains with Neumann and Robin boundary conditions. This includes the $p$-Laplace operator for all $p in (1,infty)$, but also operators with unbounded coefficients. Based on the elliptic result we show that the corresponding parabolic problem is well-posed in the space $C(bar{Omega})$ provided that the coefficients satisfy a mild monotonicity condition. More precisely, we show that the realization of the elliptic operator in $C(bar{Omega})$ is m-accretive and densely defined. Thus it generates a non-linear strongly continuous contraction semigroup on $C(bar{Omega})$." @default.
- W4300546647 created "2022-10-03" @default.
- W4300546647 creator A5011259358 @default.
- W4300546647 date "2011-04-27" @default.
- W4300546647 modified "2023-09-30" @default.
- W4300546647 title "Quasilinear elliptic and parabolic Robin problems on Lipschitz domains" @default.
- W4300546647 doi "https://doi.org/10.48550/arxiv.1104.5125" @default.
- W4300546647 hasPublicationYear "2011" @default.
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