Noncoercive quasilinear elliptic operators with singular lower order terms

TL;DR

This paper studies noncoercive quasilinear elliptic operators with singular lower order terms, proving existence of solutions to Dirichlet and obstacle problems, and demonstrating higher integrability under regular data.

Contribution

It introduces a framework for analyzing noncoercive elliptic operators with singular lower order terms in Marcinkiewicz spaces, including existence and regularity results.

Findings

Existence of solutions to Dirichlet problems for noncoercive operators

Solution existence for associated obstacle problems

Higher integrability of solutions with more regular data

Abstract

We consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in Marcinkiewicz spaces. We prove the existence of a solution to the corresponding Dirichlet problem. The associated obstacle problem is also solved. Finally, we show higher integrability of a solution to the Dirichlet problem when the datum is more regular.