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 {−div(a(x,u(x))Du(x))=f(x), in Ω,u(x)=0, on ∂Ω,\begin{cases} -\text{div} (a(x,u(x)) Du (x)) =f(x), & \text { in } \Omega, \\[1mm] u(x)=0, & \text { on } \partial \Omega, \end{cases} where α(1+∣u∣)θ≤a(x,s)≤β\displaystyle\frac {\alpha}{(1+|u|) ^\theta} \le a(x,s)\le \beta with 0<α≤β<∞0<\alpha \le \beta <\infty and 0≤θ<10\le \theta <1. The method to derive regularity seems to be simpler than the classical ones.

Author information

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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

Keywords

  • Stampacchia Lemma
  • generalization
  • degenerate elliptic equation
  • regularity

Mathematics Subject Classification

35J70

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Suggested citation

H. Gao, J. Zhang, H. Ma. “A Generalization of the Stampacchia Lemma and Applications.” Journal of Convex Analysis 33 (2026), No. 1&2, 1–12. https://doi.org/10.68381/jca33001

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.