A Generalization of Stampacchia Lemma and Applications

We present a generalization of Stampacchia Lemma and give applications to regularity property of weak and entropy solutions of degenerate elliptic equations of the form $$\{\begin{array}{ll}-div(a(x,u(x))Du(x))=f(x),& \text{mbox}in\mathrm{\Omega },\\ u(x)=0,& \text{mbox}on\mathrm{\partial }\mathrm{\Omega },\end{array}$$ where $$\frac{\alpha }{(1+\mathrm{\mid }u\mathrm{\mid }{)}^{\theta }}\le a(x,s)\le \beta$$ with $0<\alpha \le \beta <\mathrm{\infty }$ and $0\le \theta <1$.