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.

M-Convergence of p-fractional energies in irregular domains / Lancia, Maria Rosaria; Creo, Simone; Vernole, Paola. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - (2021).

M-Convergence of p-fractional energies in irregular domains

Maria Rosaria Lancia;Simone Creo;Paola Vernole
2021

Abstract

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.
Fractional p-Laplacian; fractal domains; fractional Green formula; M-convergence
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M-Convergence of p-fractional energies in irregular domains / Lancia, Maria Rosaria; Creo, Simone; Vernole, Paola. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - (2021).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1470856
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