Strong Unique Continuation from the Boundary for the Spectral Fractional Laplacian
被引:3
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作者:
De Luca, Alessandra
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Univ Ca Foscari Venezia, Dipartimento Sci Mol & Nanosistemi, Via Torino 155, I-30172 Venice, ItalyUniv Ca Foscari Venezia, Dipartimento Sci Mol & Nanosistemi, Via Torino 155, I-30172 Venice, Italy
De Luca, Alessandra
[1
]
Felli, Veronica
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机构:
Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, ItalyUniv Ca Foscari Venezia, Dipartimento Sci Mol & Nanosistemi, Via Torino 155, I-30172 Venice, Italy
Felli, Veronica
[2
]
Siclari, Giovanni
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机构:
Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, ItalyUniv Ca Foscari Venezia, Dipartimento Sci Mol & Nanosistemi, Via Torino 155, I-30172 Venice, Italy
Siclari, Giovanni
[2
]
机构:
[1] Univ Ca Foscari Venezia, Dipartimento Sci Mol & Nanosistemi, Via Torino 155, I-30172 Venice, Italy
[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, Italy
We investigate unique continuation properties and asymptotic behaviour at boundary points for solutions to a class of elliptic equations involving the spectral fractional Laplacian. An extension procedure leads us to study a degenerate or singular equation on a cylinder, with a homogeneous Dirichlet boundary condition on the lateral surface and a non-homogeneous Neumann condition on the basis. For the extended problem, by an Almgren-type monotonicity formula and a blow-up analysis, we classify the local asymptotic profiles at the edge where the transition between boundary conditions occurs. Passing to traces, an analogous blow-up result and its consequent strong unique continuation property is deduced for the nonlocal fractional equation.
机构:
Hiroshima Univ, Fac Integrated Arts & Sci, Div Math & Informat, Higashihiroshima 739, JapanHiroshima Univ, Fac Integrated Arts & Sci, Div Math & Informat, Higashihiroshima 739, Japan