Jehan Oh

Regularity results of the thin obstacle problem for the p(x)-Laplacian

Abstract We study thin obstacle problems involving the energy functional with p ( x ) -growth. We prove higher integrability and Holder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent p ( x ) is Holder continuous.

Global Morrey regularity for asymptotically regular elliptic equations

Abstract We establish the global Morrey regularity and continuity results for solutions to nonlinear elliptic equations over bounded nonsmooth domains. The novelty of our contribution is that the principal part of the operator is assumed to be merely asymptotically regular with respect to the gradient of a solution, which means that it behaves like the p -Laplacian operator for large values, while the lower order terms satisfy controlled growth conditions with respect to variables modeled by the functions from Morrey spaces. Our results extend to a larger class of degenerate and singular elliptic equations from by now regular problems in the literature.

Global gradient estimates for asymptotically regular problems of p(x)-Laplacian type

We study an asymptotically regular problem of p(x)-Laplacian type with discontinuous nonlinearity in a nonsmooth bounded domain. A global Calderon–Zygmund estimate is established for such a nonlinear elliptic problem with nonstandard growth under the assumption that the associated nonlinearity has a more general kind of the asymptotic behavior near the infinity with respect to the gradient variable. We also address an optimal regularity requirement on the nonlinearity as well as a minimal geometric assumption on the boundary of the domain for the nonlinear Calderon–Zygmund theory in the setting of variable exponent Sobolev spaces.