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Abstract
We consider a Dirichlet to Neumann operator La arising in a model for water waves, with a nonlocal parameter a ∈ (−1, 1). We deduce the expression of the operator in terms of the Fourier transform, highlighting a local behaviour for small frequencies and a nonlocal behaviour for large frequencies. We further investigate the Γ-convergence of the energy associated to the equation La(u) = W(u), where W is a double-well potential. When a ∈ (−1, 0] the energy Γconverges to the classical perimeter, while for a ∈ (0, 1) the Γ-limit is a new nonlocal operator, that in dimension n = 1 interpolates the classical and the nonlocal perimeter.
Original language | English |
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Pages (from-to) | 5997-6025 |
Number of pages | 29 |
Journal | Nonlinearity |
Volume | 33 |
Issue number | 11 |
DOIs | |
Publication status | Published - Nov 2020 |
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