Local and global minimizers for a variational energy involving a fractional norm

Giampiero Palatucci, Ovidiu Savin, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

101 Citations (Scopus)

Abstract

We study existence, uniqueness, and other geometric properties of the minimizers of the energy functional where {double pipe}u{double pipe} Hs(Ω) denotes the total contribution from Ω in the H s norm of u and W is a double-well potential. We also deal with the solutions of the related fractional elliptic Allen-Cahn equation on the entire space ℝn. The results collected here will also be useful for forthcoming papers, where the second and the third author will study the Γ-convergence and the density estimates for level sets of minimizers.

Original languageEnglish
Pages (from-to)673-718
Number of pages46
JournalAnnali di Matematica Pura ed Applicata
Volume192
Issue number4
DOIs
Publication statusPublished - Aug 2013
Externally publishedYes

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