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.

Author information

Contact details are reproduced from the original publication and may be historical.

Simone Creo

Dip. di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università, Roma, Italy

Paola Vernole

Dip. di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università, Roma, Italy

Keywords

  • Fractional p-Laplacian
  • fractal domains
  • fractional Green formula
  • M-convergence
  • nonlinear semigroups
  • dynamical boundary conditions

Mathematics Subject Classification

35R11, 35B40; 28A80, 47H20, 47J35

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Suggested citation

S. Creo, M. R. Lancia, P. Vernole. “M-Convergence of p-Fractional Energies in Irregular Domains.” Journal of Convex Analysis 28 (2021), No. 2, 509–534. https://doi.org/10.68381/jca28029

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.