Equivalence of weak and viscosity solutions in fractional non-homogeneous problems

TL;DR

This paper proves that weak and viscosity solutions are equivalent for a class of fractional p-Laplacian equations with non-homogeneous terms depending on space, the solution, and fractional derivatives, unifying two solution concepts.

Contribution

It establishes the equivalence between weak and viscosity solutions for fractional non-homogeneous problems involving the fractional p-Laplacian, clarifying solution frameworks.

Findings

Weak and viscosity solutions are equivalent for the considered equations.

The results unify different approaches to fractional PDEs.

The work extends the understanding of solution concepts in fractional non-local problems.

Abstract

We establish the equivalence between the notions of weak and viscosity solutions for non-homogeneous equations whose main operator is the fractional p-Laplacian and the lower order term depends on $x$, $u$ and $D_s^p u$, being the last one a type of fractional derivative.