A note on a Pohozaev identity for the fractional Green function

TL;DR

This paper derives a Pohozaev-type identity for the fractional Green function, extending classical results to fractional settings and complementing recent work on the fractional Robin function's gradient representation.

Contribution

It introduces a novel Pohozaev identity for fractional Green functions, bridging classical and fractional analysis and enhancing understanding of fractional boundary value problems.

Findings

Established a Pohozaev identity for fractional Green functions.

Extended classical Pohozaev results to fractional operators.

Connected the identity with recent gradient representation formulas.

Abstract

We get a Pohozaev-type identity for the fractional Green function, which extends to the fractional setting a classical result by Brezis and Peletier. Our result complements with some more recent ones obtained by Djitte and Sueur concerning a representation formula for the gradient of the fractional Robin function.