| Abstract: |
| In this talk, we study the existence and uniqueness of weak solutions to Dirichlet boundary value problems driven by a nonlocal operator in divergence form with data in $L^1(\Omega)$ that are suitably dominated.
Moreover, we show that, as $s \nearrow 1$, the nonlocal solutions converge to the solution of the corresponding local problem, thereby recovering the classical theory as a limit case.
The results presented in this talk are based on \cite{MR5007887}.
\begin{thebibliography}{99}
\bib{MR5007887}
Arcoya, David,
Dipierro, Serena,
Proietti Lippi, Edoardo,
Sportelli, Caterina,
Valdinoci, Enrico,
Nonlocal operators in divergence form and existence theory for
integrable data,
J. Funct. Anal.,
290,
2026,
7,
Paper No. 111317, 58,
issn 0022-1236,
MR{5007887},
doi{10.1016/j.jfa.2025.111317},
\end{thebibliography} |
|