Existence and regularity for a general class of quasilinear elliptic problems involving the Hardy potential

TL;DR

This paper proves the existence and regularity of solutions for a broad class of quasilinear elliptic problems with Hardy potential, highlighting the regularizing influence of first order terms and establishing integral estimates for second derivatives.

Contribution

It introduces a general framework demonstrating the regularizing effect of first order terms in quasilinear elliptic problems with Hardy potential and derives sharp integral estimates.

Findings

Existence of energy solutions for problems with Hardy potential and L^1 data.

Regularizing effect of first order terms in the equations.

Sharp local and global integral estimates for second derivatives.

Abstract

In a very general quasilinear setting, we show that the regularizing effect of a first order term causes the existence of energy solutions for problems involving the Hardy potential and $L^1$ data. In the same setting we study sharp (local and global) integral estimates for the second derivatives of the solutions.