Regularity for anisotropic elliptic equations with degenerate coercivity

Abstract

This paper deals with boundary value problems of the form −∑i=1nDi(ai(x,u(x),Du(x)))=f(x),x∈Ω,u(x)=0,x∈∂Ω. Assume that there exist c1,ν,θ>0 such that for almost all x∈Ω and all (s,z)∈R×Rn, |ai(x,s,z)|≤c11+|zi|pi−1,i=1,…,n, and ν∑i=1n|zi|pi(1+|s|)θ≤∑i=1nai(x,s,z)zi. We let f∈Lm(Ω) and we derive regularity results for weak solutions.