Journal of Convex Analysis 33 (2026), No. 1&2, 001--012
Copyright Heldermann Verlag 2026
A Generalization of the Stampacchia Lemma and Applications
Hongya Gao
College of Mathematics and Information Science, Hebei University, Baoding, China
Jiaxiang Zhang
Department of Mathematics, Beijing Jiaotong University, Beijing, China
Hongyan Ma
College of Mathematics and Information Science, Hebei University, Baoding, China
mahongyan@hbu.edu.cn
[Abstract-pdf]
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 $$ \begin{cases} -\mbox{div} (a(x,u(x)) Du (x)) =f(x), & \mbox { in } \Omega, \\[1mm] u(x)=0, & \mbox { on } \partial \Omega, \end{cases} $$ where\ \ $\displaystyle\frac {\alpha}{(1+|u|) ^\theta} \le a(x,s)\le \beta$ \,with \,$0<\alpha \le \beta <\infty$ \,and \,$0\le \theta <1$.\ \ The method to derive regularity seems to be simpler than the classical ones.
Keywords: Stampacchia Lemma, generalization, degenerate elliptic equation, regularity.
MSC: 35J70.
[ Fulltext-pdf (126 KB)] for subscribers only.