A Generalization of Stampacchia Lemma and Applications

Abstract

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 $$ \left\{ \begin{array}{llll} -\mbox{div} (a(x,u(x)) Du (x)) =f(x), & \mbox { in } Ω, \\ u(x)=0, & \mbox { on } \partial Ω, \end{array} \right. $$ where $$\frac{\alpha }{(1+|u|{)}^{\theta }}\le a(x,s)\le \beta$$ with $0<\alpha \le \beta <\infty$ and $0\le \theta <1$.

10 pages