Weak and viscosity solutions for non-homogeneous fractional equations in Orlicz spaces

Abstract

In this paper, we consider non-homogeneous fractional equations in Orlicz spaces, with a source depending on the spatial variable, the unknown function, and its fractional gradient. The latter is adapted to the Orlicz framework. The main contribution of the article is to establish the equivalence between weak and viscosity solutions for such equations.

36 pages

Cited by in corpus (1)

• The trace fractional Laplacian and the mid-range fractional Laplacian