Local and global behaviour of nonlinear equations with natural growth terms

TL;DR

This paper investigates the pointwise behavior of positive solutions to quasi-linear elliptic equations with natural growth terms, providing optimal estimates using local Wolff's potentials under minimal regularity assumptions.

Contribution

It introduces new optimal pointwise estimates for solutions based on local Wolff's potentials, advancing understanding of nonlinear elliptic equations with minimal regularity.

Findings

Derived optimal pointwise estimates for solutions

Connected solutions' behavior to local Wolff's potentials

Applicable under minimal regularity conditions

Abstract

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.