Uniqueness for fractional parabolic and elliptic equations with drift

TL;DR

This paper studies the uniqueness of solutions in weighted Lebesgue spaces for a class of fractional parabolic and elliptic equations that include a drift term.

Contribution

It establishes conditions for uniqueness of solutions to fractional PDEs with drift in weighted Lebesgue spaces, advancing understanding of these equations.

Findings

Proves uniqueness under specific weighted space conditions

Identifies key properties of fractional operators with drift

Provides theoretical framework for fractional PDEs with drift

Abstract

We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.