M-Convergence of p-Fractional Energies in Irregular Domains

We study the asymptotic behavior of anomalous p-fractional energies in bad domains via the M-convergence. These energies arise naturally when studying Robin-Venttsel' problems for the regional fractional p-Laplacian. We provide a suitable notion of fractional normal derivative on irregular sets via a fractional Green formula as well as existence and uniqueness results for the solution of the Robin-Venttsel' problem by a semigroup approach. Markovianity properties of the associated semigroup are proved.