We consider a boundary value problem driven by the p-fractional Laplacian with nonlocal Robin boundary conditions and we provide necessary and sufficient conditions which ensure the existence of a unique positive (weak) solution. The results proved in this paper can be considered a first step towards a complete generalization of the classical result by Brezis and Oswald (Nonlinear Anal 10:55–64, 1986) to the nonlocal setting.
Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions / Mugnai D.; Pinamonti A.; Vecchi E.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 59:2(2020), pp. 43.1-43.25. [10.1007/s00526-020-1708-8]
Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions
Vecchi E.
2020
Abstract
We consider a boundary value problem driven by the p-fractional Laplacian with nonlocal Robin boundary conditions and we provide necessary and sufficient conditions which ensure the existence of a unique positive (weak) solution. The results proved in this paper can be considered a first step towards a complete generalization of the classical result by Brezis and Oswald (Nonlinear Anal 10:55–64, 1986) to the nonlocal setting.| File | Dimensione | Formato | |
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