Entropy solutions for some elliptic problems involving the generalized p(u)-Laplacian operator

Abstract

In this paper, we study the existence of entropy solutions for some generalized elliptic p(u)-Laplacian problem when p(u) is a local quantity. We get the results by assuming the right-hand side function f to be an integrable function, and by using the regularization approach combined with the theory of Sobolev spaces with variable exponents.