On a fractional sublinear elliptic equation with a variable coefficient

TL;DR

This paper investigates the existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with variable coefficients in the whole space, connecting it to related fractional linear and porous medium equations.

Contribution

It introduces new results on existence and uniqueness for fractional elliptic equations with variable coefficients, linking them to fractional linear and porous medium equations.

Findings

Existence of bounded solutions under certain conditions.

Uniqueness of solutions established via related fractional porous medium equations.

Connections made between elliptic, linear, and porous medium fractional equations.

Abstract

We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the proof of uniqueness relies on uniqueness of solutions to an associated fractional porous medium equation with variable density.