JournalsifbVol. 9, No. 1pp. 133–148

Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraint

  • Eduardo V. Teixeira

    Universidade Federal do Ceará, Fortaleza, Brazil
Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraint cover
Download PDF

Abstract

In this paper we study qualitative geometric properties of optimal configurations to a variational problem with free boundary, under suitable assumptions on a fixed boundary. More specifically, we study the problem of minimizing the flow of heat given by DΓ(uμ)dσ\int_{\partial D} \Gamma (u_\mu) d\sigma, where DD is a fixed domain and uu is the potential of a domain ΩD\Omega \supset \partial D, with a prescribed volume on ΩD\Omega \setminus D. Our main goal is to establish uniqueness and symmetry results when D\partial D has a given geometric property. Full regularity of the free boundary is obtained under these symmetry conditions imposed on the fixed boundary.

Cite this article

Eduardo V. Teixeira, Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraint. Interfaces Free Bound. 9 (2007), no. 1, pp. 133–148

DOI 10.4171/IFB/159