Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity
-
Sun-Sig Byun
,
Jihoon Ok
Abstract
We consider a nonlinear elliptic problem in divergence form, with nonstandard growth conditions, on a bounded domain. We obtain the global Calderón–Zygmund type gradient estimates for the weak solution of such a problem in the setting of Lebesgue and Sobolev spaces with variable p(x) exponents, in the case that the nonlinearity of the coefficients is allowed to be discontinuous and the domain goes beyond the Lipschitz category. We assume that the nonlinearity has small BMO semi-norms and the boundary of the domain satisfies the so-called δ-Reifenberg flatness condition. These conditions on the nonlinearity and the boundary are weaker than those reported in other studies in the literature.
Funding source: National Research Foundation of Korea (NRF)
Award Identifier / Grant number: 2012-047030
Funding statement:
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity
- Universal and homogeneous embeddings of dual polar spaces of rank 3 defined over quadratic alternative division algebras
- Mixing operators and small subsets of the circle
- Singularities on the base of a Fano type fibration
- Stable representation homology and Koszul duality
- An inverse spectral problem for a star graph of Krein strings
- Uniqueness of self-similar shrinkers with asymptotically cylindrical ends
- Ultraproducts, QWEP von Neumann algebras, and the Effros–Maréchal topology
Artikel in diesem Heft
- Frontmatter
- Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity
- Universal and homogeneous embeddings of dual polar spaces of rank 3 defined over quadratic alternative division algebras
- Mixing operators and small subsets of the circle
- Singularities on the base of a Fano type fibration
- Stable representation homology and Koszul duality
- An inverse spectral problem for a star graph of Krein strings
- Uniqueness of self-similar shrinkers with asymptotically cylindrical ends
- Ultraproducts, QWEP von Neumann algebras, and the Effros–Maréchal topology
