Data di Pubblicazione:
2015
Citazione:
On a fractional harmonic replacement / S. Dipierro, E. Valdinoci. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 35:8(2015), pp. 3377-3392. [10.3934/dcds.2015.35.3377]
Abstract:
Given s ∈ (0, 1), we consider the problem of minimizing the fractional Gagliardo seminorm in Hs with prescribed condition outside the ball and under the further constraint of attaining zero value in a given set K. We investigate how the energy changes in dependence of such set. In particular, under mild regularity conditions, we show that adding a set A to K increases the energy of at most the measure of A (this may be seen as a perturbation result for small sets A). Also, we point out a monotonicity feature of the energy with respect to the prescribed sets and the boundary conditions.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Energy estimates; Fractional Sobolev spaces; Harmonic replacement; Discrete Mathematics and Combinatorics; Applied Mathematics; Analysis
Elenco autori:
S. Dipierro, E. Valdinoci
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