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Journal of Convex Analysis 28 (2021), No. 2, 509--534
Copyright Heldermann Verlag 2021



M-Convergence of p-Fractional Energies in Irregular Domains

Simone Creo
Dip. di Scienze di Base e Applicate per l'Ingegneria, Sapienza UniversitÓ, Roma, Italy

Maria Rosaria Lancia
Dip. di Scienze di Base e Applicate per l'Ingegneria, Sapienza UniversitÓ, Roma, Italy
maria.lancia@sbai.uniroma1.it

Paola Vernole
Dip. di Scienze di Base e Applicate per l'Ingegneria, Sapienza UniversitÓ, Roma, Italy



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.

Keywords: Fractional p-Laplacian, fractal domains, fractional Green formula, M-convergence, nonlinear semigroups, dynamical boundary conditions.

MSC: 35R11, 35B40; 28A80, 47H20, 47J35.

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