An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term

TL;DR

This paper investigates an elliptic boundary value problem with degenerate coercivity and a singular quadratic gradient term, revealing that the singularity can have a regularizing effect on solutions.

Contribution

It demonstrates that even with a singular lower order term, solutions exhibit regularization, advancing understanding of elliptic equations with degenerate and singular features.

Findings

Singular lower order term can have a regularizing effect

Existence of solutions under degenerate coercivity

Insights into elliptic equations with singular growth

Abstract

In this paper we study a Dirichlet problem for an elliptic equation with degenerate coercivity and a singular lower order term with natural growth with respect to the gradient. We will show that, even if the lower order term is singular, it has some regularizing effects on the solutions