Existence and uniqueness of solutions to some anisotropic elliptic equations with a singular convection term

TL;DR

This paper establishes the existence and uniqueness of weak solutions for a class of anisotropic elliptic equations with singular convection terms, providing key a priori estimates and regularity results.

Contribution

It introduces new conditions on convection coefficients in Marcinkiewicz spaces ensuring solution existence and uniqueness for anisotropic elliptic equations.

Findings

Existence and uniqueness of weak solutions proven.

Derived useful a priori estimates.

Established regularity results.

Abstract

We prove the existence and uniqueness of weak solutions to a class of anisotropic elliptic equations with coefficients of convection term belonging to some suitable Marcinkiewicz spaces. Some useful a priori estimates and regularity results are also derived.