Analysis on the junctions of domain walls

Luis A. Caffarelli, Fang-Hua Lin

Research output: Contribution to journalArticle

Abstract

In this paper, we study the local structure and the smoothness of singularities of free boundaries in an optimal partition problem for the Dirichlet eigenvalues. We prove that there is a unique homogeneous blow up(tangent map) at each singular point in the interior of the free boundary. As a consequence we obtain the rectifiability as well as local structures of singularities.

Original languageEnglish (US)
Pages (from-to)915-929
Number of pages15
JournalDiscrete and Continuous Dynamical Systems
Volume28
Issue number3
DOIs
StatePublished - Nov 2010

Fingerprint

Domain walls
Domain Wall
Local Structure
Free Boundary
Rectifiability
Singularity
Dirichlet Eigenvalues
Optimal Partition
Singular Point
Tangent line
Blow-up
Smoothness
Interior

Keywords

  • Calculus of variations
  • Free boundaries
  • Montonicity formula

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Analysis on the junctions of domain walls. / Caffarelli, Luis A.; Lin, Fang-Hua.

In: Discrete and Continuous Dynamical Systems, Vol. 28, No. 3, 11.2010, p. 915-929.

Research output: Contribution to journalArticle

Caffarelli, Luis A. ; Lin, Fang-Hua. / Analysis on the junctions of domain walls. In: Discrete and Continuous Dynamical Systems. 2010 ; Vol. 28, No. 3. pp. 915-929.
@article{42b9dadad70c43659422b28fe146ac49,
title = "Analysis on the junctions of domain walls",
abstract = "In this paper, we study the local structure and the smoothness of singularities of free boundaries in an optimal partition problem for the Dirichlet eigenvalues. We prove that there is a unique homogeneous blow up(tangent map) at each singular point in the interior of the free boundary. As a consequence we obtain the rectifiability as well as local structures of singularities.",
keywords = "Calculus of variations, Free boundaries, Montonicity formula",
author = "Caffarelli, {Luis A.} and Fang-Hua Lin",
year = "2010",
month = "11",
doi = "10.3934/dcds.2010.28.915",
language = "English (US)",
volume = "28",
pages = "915--929",
journal = "Discrete and Continuous Dynamical Systems",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "3",

}

TY - JOUR

T1 - Analysis on the junctions of domain walls

AU - Caffarelli, Luis A.

AU - Lin, Fang-Hua

PY - 2010/11

Y1 - 2010/11

N2 - In this paper, we study the local structure and the smoothness of singularities of free boundaries in an optimal partition problem for the Dirichlet eigenvalues. We prove that there is a unique homogeneous blow up(tangent map) at each singular point in the interior of the free boundary. As a consequence we obtain the rectifiability as well as local structures of singularities.

AB - In this paper, we study the local structure and the smoothness of singularities of free boundaries in an optimal partition problem for the Dirichlet eigenvalues. We prove that there is a unique homogeneous blow up(tangent map) at each singular point in the interior of the free boundary. As a consequence we obtain the rectifiability as well as local structures of singularities.

KW - Calculus of variations

KW - Free boundaries

KW - Montonicity formula

UR - http://www.scopus.com/inward/record.url?scp=77955320557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955320557&partnerID=8YFLogxK

U2 - 10.3934/dcds.2010.28.915

DO - 10.3934/dcds.2010.28.915

M3 - Article

VL - 28

SP - 915

EP - 929

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 3

ER -