Rearrangement optimization problems with free boundary

B. Emamizadeh, M. Marras

Research output: Journal PublicationArticlepeer-review

5 Citations (Scopus)


This article is concerned with three optimization problems. In the first problem, a functional is maximized with respect to a set that is the weak closure of a rearrangement class; that is, a set comprising rearrangements of a prescribed function. Questions regarding existence, uniqueness, symmetry, and local minimizers are addressed. The second problem is of maximization type related to a Poisson boundary value problem. After defining a relevant function, we prove it is differentiable and derive an explicit formula for its derivative. Further, using the co-area formula, we establish a free boundary result. The third problem is the minimization version of the second problem.

Original languageEnglish
Pages (from-to)404-422
Number of pages19
JournalNumerical Functional Analysis and Optimization
Issue number4
Publication statusPublished - 3 Apr 2014


  • Co-area formula
  • Existence
  • Free boundary
  • Local minimizers
  • Maximization
  • Minimization
  • Rearrangements
  • Symmetry
  • Uniqueness

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization


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