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- W2949204771 abstract "We derive global gradient estimates for $W^{1,p}_0(Omega)$-weak solutions to quasilinear elliptic equations of the form $$ mathrm{div,}mathbf{a}(x,u,Du)=mathrm{div,}(|F|^{p-2}F) $$ over $n$-dimensional Reifenberg flat domains. The nonlinear term of the elliptic differential operator is supposed to be small-BMO with respect to $x$ and Holder continuous in $u.$ In the case when $pgeq n,$ we allow only continuous nonlinearity in $u.$ Our result highly improves the known regularity results available in the literature. In fact, we are able not only to weaken the regularity requirement on the nonlinearity in $u$ from Lipschitz continuity to Holder one, but we also find a very lower level of geometric assumptions on the boundary of the domain to ensure global character of the obtained gradient estimates." @default.
- W2949204771 created "2019-06-27" @default.
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- W2949204771 date "2017-03-29" @default.
- W2949204771 modified "2023-09-25" @default.
- W2949204771 title "Global Sobolev regularity for general elliptic equations of $p$-Laplacian type" @default.
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- W2949204771 doi "https://doi.org/10.48550/arxiv.1703.09918" @default.
- W2949204771 hasPublicationYear "2017" @default.
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