Special Session 93: Local and nonlocal elliptic boundary value problems

The superposition of operators of mixed fractional order and their applications
Caterina Sportelli
Universidad de Granada
Spain
Co-Author(s):    
Abstract:
In this talk we introduce the superposition operator \begin{equation}\label{superposition} \int_{[0, 1]} (-\Delta)^s u \, d\mu(s), \end{equation} where $\mu$ denotes a (Borel) signed measure on the fractional interval $[0, 1]$. We discuss the existence of solutions for some problems in presence of the operator \eqref{superposition} and subject to different types of boundary conditions. These results are part of some joint works with Serena Dipierro, Enrico Valdinoci and Kanishka Perera.