Albo Carlos Cavalheiro, The existence of entropy solutions for nonlinear degenerate elliptic equations, Vol. 2020 (2020), Article ID 38, pp. 1-14

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DOI: 10.23952/jnfa.2020.38

Received August 11, 2020; Accepted September 9, 2020; September 17, 2020

Abstract. In this article, we prove the existence of entropy solutions for the Dirichlet problem
$-div[{\mathcal{A}}(x,\nabla u){\omega}_1 +{\mathcal{B}}(x,u,\nabla u){\omega}_2] = f(x), in\ \Omega,$
$u(x) = 0, on\ \partial\Omega,$
where $\Omega$ is a bounded open set of $\mathbb{R}^N$, $N\geq 2$ and $f\in L^1(\Omega)$. An example is provided to support our result.