Optimal rearrangement problem and normalized obstacle problem in the fractional setting

Optimal rearrangement problem and normalized obstacle problem in the fractional setting

We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (– , 0 < < 1, and the Gagliardo seminorm | . We prove the existence of the unique minimizer, analyze its properties as well as derive the non-local and highly non-linear PDE it satisfies which h...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Advances in nonlinear analysis 2020-03, Vol.9 (1), p.1592-1606
Hauptverfasser: Bonder, Julián Fernández, Cheng, Zhiwei, Mikayelyan, Hayk
Format: Artikel
Sprache:eng
Schlagworte:
35J60
35R11
Fractional partial differential equations
Obstacle problem
Optimization problems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (– , 0 < < 1, and the Gagliardo seminorm | . We prove the existence of the unique minimizer, analyze its properties as well as derive the non-local and highly non-linear PDE it satisfies which happens to be the fractional analogue of the normalized obstacle problem =
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2020-0067