Data di Pubblicazione:
2015
Citazione:
A nonlocal free boundary problem / S. Dipierro, O. Savin, E. Valdinoci. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 47:6(2015), pp. 4559-4605. [10.1137/140999712]
Abstract:
Given s,σ ∈ (0,1) and a bounded domain Ω ⊂ ℝn, we consider the following minimization problem of s-Dirichlet-plus-σ-perimeter-type | u|Hsℝ2n\(Ωc)2) + Perσ(u > 0,Ω), where [·]hs is the fractional Gagliardo seminorm and Perσ is the fractional perimeter. Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones, and a trivialization result for the flat case. The classical free boundary problems are limit cases of the one that we consider in this paper, as s ↗ 1, σ ↗ 1, or σ 0.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Classification of cones; Fractional perimeter; Minimization problem; Monotonicity formula; Analysis; Applied Mathematics; Computational Mathematics
Elenco autori:
S. Dipierro, O. Savin, E. Valdinoci
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