TOPOLOZICAL DERIVATIVE OF THE FRACTIONAL $p$-LAPLACIAN OPERATORS

The objective of this article is the study of topological optimization problems with p-Laplacian operators, i.e. $(-\Delta)_p^s$ where $0<s<1$ and $p\geq2.$ In [22], we began studying this problem to determine the shape derivative. In the same paper, we studied existence results using s-gamma convergence. In this paper, we work with the open class checking the $\epsilon -$c\^one property to obtain that the existence of an optimal shape. And finally we found the topological derivative of the functional through the minmax method.