Existence of solutions for degenerate quasilinear elliptic equations

摘要

This paper deals with a class of degenerate quasilinear elliptic equations of the form -div(a(x,u,?u)=g-div(f), where a(x,u,?u) is allowed to be degenerate with the unknown u. We prove existence of bounded solutions under some hypothesis on f and g. Moreover we prove that there exists a renormalized solution in the case where g∈L1(Ω) and f∈(Lp′(Ω))N.