Partial Regularity for Optimal Design Problems Involving Both Bulk and Surface Energies

Research output: Contribution to journalArticle

Abstract

This paper studies a class of variational problems which involving both bulk and surface energies. The bulk energy is of Dirichlet type though it can be in very general forms allowing unknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integral which is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularity of the free interface of such problems.

Original languageEnglish (US)
Pages (from-to)137-158
Number of pages22
JournalChinese Annals of Mathematics. Series B
Volume20
Issue number2
StatePublished - 1999

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Partial Regularity
Surface Energy
Interfacial energy
Regularity Theory
Set Partitioning
Existence Theory
Variational Problem
Dirichlet
Regularity
Scalar
Unknown
Arbitrary
Energy
Optimal design
Class
Form

Keywords

  • Nonlinear variational problems
  • Optimal design problem
  • Partial regularity

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "Partial Regularity for Optimal Design Problems Involving Both Bulk and Surface Energies",
abstract = "This paper studies a class of variational problems which involving both bulk and surface energies. The bulk energy is of Dirichlet type though it can be in very general forms allowing unknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integral which is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularity of the free interface of such problems.",
keywords = "Nonlinear variational problems, Optimal design problem, Partial regularity",
author = "Fang-Hua Lin and Robert Kohn",
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AB - This paper studies a class of variational problems which involving both bulk and surface energies. The bulk energy is of Dirichlet type though it can be in very general forms allowing unknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integral which is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularity of the free interface of such problems.

KW - Nonlinear variational problems

KW - Optimal design problem

KW - Partial regularity

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