Existence of solutions for some noncercive elliptic problems involving derivatives of nonlinear terms

TL;DR

This paper investigates the existence of solutions for certain nonlinear elliptic problems with degenerate coercivity, providing conditions under which solutions exist in various weak senses.

Contribution

It establishes the existence of solutions for nonlinear elliptic equations with degenerate coercivity, considering different solution concepts based on growth conditions.

Findings

Existence of W^{1,1}_0 solutions under specific conditions

Solutions can be distributional or entropic depending on growth assumptions

Results extend the understanding of degenerate elliptic problems

Abstract

We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a W^{1,1}_0 solution which is distributional or entropic, according to the growth assumptions on a lower order term in divergence form.