Estimates for \(p\)-Poisson equations. (English) Zbl 0970.35035

Kilpeläinen, Tero; Li, Gongbao

Differ. Integral Equ. 13, No. 4-6, 791-800 (2000).

Estimates for solutions of equations whose model is \[ -\text{ div}(|\nabla u|^{p-2}\nabla u) = f \] are given. Here \(f\) denotes a function in the weak \(L^q\) space. As an application of the results regularity of some entropy solutions are proved.

Reviewer: Giuseppe Di Fazio (Catania)

MSC:

35J60	Nonlinear elliptic equations
31C45	Other generalizations (nonlinear potential theory, etc.)
35B45	A priori estimates in context of PDEs
35B65	Smoothness and regularity of solutions to PDEs

Keywords:

elliptic equations; entropy solutions