We study a nonlocal Robin–Venttsel’-type problem for the regional fractional p-Laplacian in an extension domain Ω with boundary a d-set. We prove existence and uniqueness of a strong solution via a semigroup approach. Markovianity and ultracontractivity properties are proved. We then consider the elliptic problem. We prove existence, uniqueness and global boundedness of the weak solution.

Fractional (s, p)-Robin–Venttsel’ problems on extension domains / Creo, S.; Lancia, M. R.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 28:3(2021). [10.1007/s00030-021-00692-w]

Fractional (s, p)-Robin–Venttsel’ problems on extension domains

Creo S.;Lancia M. R.
2021

Abstract

We study a nonlocal Robin–Venttsel’-type problem for the regional fractional p-Laplacian in an extension domain Ω with boundary a d-set. We prove existence and uniqueness of a strong solution via a semigroup approach. Markovianity and ultracontractivity properties are proved. We then consider the elliptic problem. We prove existence, uniqueness and global boundedness of the weak solution.
Dynamical boundary conditions; Extension domains; Fractional Green formula; Fractional p-Laplacian; Nonlinear semigroups; Ultracontractivity
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Fractional (s, p)-Robin–Venttsel’ problems on extension domains / Creo, S.; Lancia, M. R.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 28:3(2021). [10.1007/s00030-021-00692-w]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1551099
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