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

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.


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