Optimal rearrangement problem and normalized obstacle problem in the fractional setting

Julián Fernández Bonder, Zhiwei Cheng, Hayk Mikayelyan

Research output: Journal PublicationArticlepeer-review

4 Citations (Scopus)

Abstract

We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (-Δ)s, 0 < s < 1, and the Gagliardo seminorm jujs. We prove the existence of the unique minimizer, analyze its properties as well as derive the non-local and highly non-linear PDE it satises -(-Δ)sU - x-(-Δ)sU+; 1 =U>0g, which happens to be the fractional analogue of the normalized obstacle problem Δu = xu>0.

Original languageEnglish
Pages (from-to)1592-1606
Number of pages15
JournalAdvances in Nonlinear Analysis
Volume9
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • Fractional partial differential equations
  • Obstacle problem
  • Optimization problems

ASJC Scopus subject areas

  • Analysis

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