## Differential and Integral Equations

### Estimates for $p$-Poisson equations

#### Abstract

We derive estimates for solutions to the equations like $$-{\operatorname{div}}(|\nabla u|^{p-2}\nabla u)=f\,,$$ where $f$ belongs to weak $L^q$ spaces. As applications of our results we show that the entropy solutions of $$-{\operatorname{div}}(|\nabla u|^{p-2}\nabla u)=|u|^{a-1}u$$ are regular provided that $0\le a < n(p-1)/(n-p)$.

#### Article information

Source
Differential Integral Equations Volume 13, Number 4-6 (2000), 791-800.

Dates
First available in Project Euclid: 21 December 2012

Kilpeläinen, Tero; Li, Gongbao. Estimates for $p$-Poisson equations. Differential Integral Equations 13 (2000), no. 4-6, 791--800.https://projecteuclid.org/euclid.die/1356061250