Journal of Mathematical Physics, Analysis, Geometry 2021, vol. 17, No 1, pp. 54-78   https://doi.org/10.15407/mag17.01.054     ( to contents , go back )

### Entropy Solutions of the Dirichlet Problem for Some Nonlinear Elliptic Degenerate Second-Order Equations

Yuliya Gorban

Vasyl' Stus Donetsk National University, 21 600-richchia Str., Vinnytsia, 21021, Ukraine
E-mail: yuliyagorban77@gmail.com

Anastasiia Soloviova

Vasyl' Stus Donetsk National University, 21 600-richchia Str., Vinnytsia, 21021, Ukraine
E-mail: nastiasoloviova1997@gmail.com

Received July 29, 2020, revised October 17, 2020.

Abstract

In the present paper, we deal with the Dirichlet problem for a model nonlinear elliptic second-order equation with degenerated (with respect to the independent variables) coefficients, lower term, and $L^1$-right-hand side. The existence of an entropy solution to the problem under consideration is proved.

Mathematics Subject Classification 2010: 35J25, 35J60, 35J70
Key words: degenerate elliptic equations, L1-right-hand side, Dirichlet problem, entropy solution, existence of solutions