Quasilinear elliptic equations with natural growth and quasilinear elliptic equations with singular drift

TL;DR

This paper establishes existence results for quasilinear elliptic equations with natural growth conditions and singular drift, using auxiliary variational inequalities as a key analytical tool.

Contribution

It introduces a novel approach employing auxiliary variational inequalities to prove existence for equations with natural growth and singular drift.

Findings

Proved existence of solutions under natural growth conditions.

Extended results to equations with singular drift.

Developed a new variational inequality method for analysis.

Abstract

We prove an existence result for a quasilinear elliptic equation satisfying natural growth conditions. As a consequence, we deduce an existence result for a quasilinear elliptic equation containing a singular drift. A key tool, in the proof, is the study of an auxiliary variational inequality playing the role of "natural constraint"