On regularity and singularity of free boundaries in obstacle problems

Fanghua Lin

doi:10.1007/s11401-009-0174-6

On regularity and singularity of free boundaries in obstacle problems

Fanghua Lin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems. This approach is based on the monotonicity of several variational integrals, the Federer-Almgren dimension reduction and stratification theorems, and some simple PDE arguments.

Original language	English (US)
Pages (from-to)	645-652
Number of pages	8
Journal	Chinese Annals of Mathematics. Series B
Volume	30
Issue number	5
DOIs	https://doi.org/10.1007/s11401-009-0174-6
State	Published - 2009

Keywords

Dimension reduction
Free boundary
Monotonicity
Uniqueness of blow-ups

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1007/s11401-009-0174-6

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title = "On regularity and singularity of free boundaries in obstacle problems",

abstract = "The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems. This approach is based on the monotonicity of several variational integrals, the Federer-Almgren dimension reduction and stratification theorems, and some simple PDE arguments.",

keywords = "Dimension reduction, Free boundary, Monotonicity, Uniqueness of blow-ups",

author = "Fanghua Lin",

note = "Funding Information: Manuscript received May 16, 2009. Published online August 10, 2009. ∗Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York 10012, USA. E-mail: linf@courant.nyu.edu ∗∗Project supported by the National Science Foundation (No. DMS 0700517).",

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PY - 2009

Y1 - 2009

N2 - The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems. This approach is based on the monotonicity of several variational integrals, the Federer-Almgren dimension reduction and stratification theorems, and some simple PDE arguments.

AB - The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems. This approach is based on the monotonicity of several variational integrals, the Federer-Almgren dimension reduction and stratification theorems, and some simple PDE arguments.

KW - Dimension reduction

KW - Free boundary

KW - Monotonicity

KW - Uniqueness of blow-ups

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SN - 0252-9599

IS - 5

ER -

On regularity and singularity of free boundaries in obstacle problems

Abstract

Keywords

ASJC Scopus subject areas

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