On Shape Optimization Theory With Fractional p-Laplacian Operators

Abstract

The focus of this paper is the investigation of shape optimization problems with operators such as fractional Laplacian and p-Laplacian operators, that is, −Δs and −Δps, where 0<s<1 and p≥2. In the admissible set of s− quasi-open, the existence of optimal shape is proved for shape derivative of the functional FΩ=fΩ,uΩ, where uΩ represents the solution of the fractional operators.