The fundamental solution of nonlinear equations with natural growth terms

TL;DR

This paper derives bilateral global bounds and examines Sobolev regularity of fundamental solutions for certain nonlinear operators with natural growth terms, advancing understanding of their behavior and regularity properties.

Contribution

It provides new bilateral bounds and Sobolev regularity results for fundamental solutions of nonlinear equations with natural growth, which were previously not well understood.

Findings

Established bilateral global bounds for fundamental solutions.

Analyzed Sobolev regularity away from the pole.

Extended understanding of nonlinear operators with natural growth.

Abstract

We find bilateral global bounds for the fundamental solutions associated with some quasilinear and fully nonlinear operators perturbed by a nonnegative zero order term with natural growth. In addition, we consider the Sobolev regularity of the fundamental solution away from its pole.