On the convergence of solutions of degenerate elliptic equations in divergence form

Abstract

It is studied the convergence of solutions of Dirichlet problems for sequences of monotone operators of the type — div (ah (x, D·)), where the functions ah verify the following degenerate coerciveness assumption $$(a_h (x,\xi _1 ) - a_h (x,\xi _2 )|\xi _1 - \xi _2 ) \geqslant \mu _h (x)|\xi _1 - \xi _2 |^p (p \geqslant 2)$$ , being (μh)h a sequence of function verifying a Muckenhoupt condition uniformly in h.