### 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 language | English (US) |
---|---|

Pages (from-to) | 137-158 |

Number of pages | 22 |

Journal | Chinese Annals of Mathematics. Series B |

Volume | 20 |

Issue number | 2 |

State | Published - 1999 |

### Fingerprint

### Keywords

- Nonlinear variational problems
- Optimal design problem
- Partial regularity

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Partial Regularity for Optimal Design Problems Involving Both Bulk and Surface Energies.** / Lin, Fang-Hua; Kohn, Robert.

Research output: Contribution to journal › Article

*Chinese Annals of Mathematics. Series B*, vol. 20, no. 2, pp. 137-158.

}

TY - JOUR

T1 - Partial Regularity for Optimal Design Problems Involving Both Bulk and Surface Energies

AU - Lin, Fang-Hua

AU - Kohn, Robert

PY - 1999

Y1 - 1999

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=0033410414&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033410414&partnerID=8YFLogxK

M3 - Article

VL - 20

SP - 137

EP - 158

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

SN - 0252-9599

IS - 2

ER -