Global gradient estimates for a general class of quasilinear elliptic equations with Orlicz growth

Baasandorj, Sumiya; Byun, Sun-Sig; Lee, Ho-Sik

doi:10.1090/proc/15585

Global gradient estimates for a general class of quasilinear elliptic equations with Orlicz growth
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by Sumiya Baasandorj, Sun-Sig Byun and Ho-Sik Lee PDF

Proc. Amer. Math. Soc. 149 (2021), 4189-4206 Request permission

Abstract:

We provide an optimal global Calderón-Zygmund theory for quasilinear elliptic equations of a very general form with Orlicz growth on bounded nonsmooth domains under minimal regularity assumptions of the nonlinearity $A=A(x,u,Du)$ in the first and second variables $(x,z)$ as well as on the boundary of the domain. Our result improves known regularity results in the literature regarding nonlinear elliptic operators depending on a given bounded weak solution.

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