Elliptic Equations with Degenerate Coercivity: Gradient Regularity

Abstract

In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is\( - div{\left( {a{\left( {x,u} \right)}Du} \right)} = f\;in\;{D}\ifmmode{'}\else$'$\fi{\left( \Omega \right)},\;f \in L^{r} {\left( \Omega \right)},\;r > 1, \) where for example, a(x,u)=(1+|u|)−θ with θ ∈ (0,1). We study the same problem for minima of functionals closely related to the previous equation.