| 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. |
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