Abstract
We prove the existence of renormalized solutions belonging to W-0(1,1)(Omega) of a class of strongly nonlinear elliptic p -Laplace type problems when 1 < p < 2 - 1/N with data of poor summability in the Lebesgue space L-m(Omega), m = N/((p - 1)N + 1). Our method consists in applying Schaefer's classical fixed point theorem relying on new estimates of the gradient of the unique renormalized solution of problems with datum in L-m(Omega).