Regularity of solutions for a class of quasilinear elliptic equations related to Caffarelli-Kohn-Nirenberg inequality

TL;DR

This paper investigates the regularity of solutions to certain quasilinear elliptic equations linked to the Caffarelli-Korn-Nirenberg inequality, establishing local boundedness and Hölder continuity using De Giorgi methods.

Contribution

It extends existing regularity results for quasilinear elliptic equations by incorporating potentials related to the Caffarelli-Korn-Nirenberg inequality.

Findings

Proves local boundedness of weak solutions

Establishes Hölder continuity of solutions

Extends classical results by Serrin and others

Abstract

This paper is concerned with a class of quasilinear elliptic equations involving some potentials related to the Caffarelli-Korn-Nirenberg inequality. We prove the local boundedness and H\"older continuity of weak solutions by using the classical De Giorgi techniques. Our result extends the results of Serrin \cite{Serrin64} and Corolado and Peral \cite{CP04}.