Superposition of fundamental solutions of second order quasilinear equations

TL;DR

This paper establishes a superposition principle for a class of second order quasilinear equations, showing that Riesz potentials of certain functions serve as subsolutions or supersolutions for key nonlinear diffusion operators.

Contribution

It introduces a superposition principle for second order quasilinear equations, extending previous results to include operators like the p-Laplacian and porous medium equation.

Findings

Riesz potentials are subsolutions or supersolutions for the operators.

The superposition principle applies to a broad class of quasilinear equations.

Includes operators such as p-Laplacian and stationary porous medium equation.

Abstract

We prove a superposition principle in the spirit of Crandall-Zhang and Lindqvist-Manfredi for a class of second order quasilinear equations. Riesz potentials of nonnegative and compactly supported continuous functions are either subsolutions or supersolutions for the operators associated to the stationary form of the doubly nonlinear diffusion equation. This class of operators includes both the p-Laplacian as well as the stationary porous medium equation.