Global W1,p(·) estimate for renormalized solutions of quasilinear equations with measure data on Reifenberg domains

Abstract

In this paper, we prove the gradient estimate for renormalized solutions to quasilinear elliptic equations with measure data on variable exponent Lebesgue spaces with BMO coefficients in a Reifenberg flat domain.

Keywords

• quasilinear equation
• measure data
• renormalized solution
• generalized lebesgue space
• 35j60
• 35j62