Differential and Integral Equations

Estimates for $p$-Poisson equations

Tero Kilpeläinen and Gongbao Li

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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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 31C45: Other generalizations (nonlinear potential theory, etc.) 35B45: A priori estimates 35B65: Smoothness and regularity of solutions


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

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