Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type

Morteza Fotouhi; Andreas Minne; Henrik Shahgholian; Georg S. Weiss

doi:10.3934/mine.2020032

Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type

Morteza Fotouhi, Andreas Minne, Henrik Shahgholian, Georg S. Weiss

Research output: Journal Publication › Article › peer-review

Abstract

The purpose of this note is to present a "new" approach to the decay rate of the solutions to the no-sign obstacle problem from the free boundary, based on Weiss-monotonicity formula. In presenting the approach we have chosen to treat a problem which is not touched earlier in the existing literature. Although earlier techniques may still work for this problem, we believe this approach gives a shorter proof, and may have wider applications.

Original language	English
Pages (from-to)	698-708
Number of pages	11
Journal	Mathematics in Engineering
Volume	2
Issue number	4
DOIs	https://doi.org/10.3934/mine.2020032
Publication status	Published - 2020
Externally published	Yes

Keywords

No-sign obstacle problem
Regularity of solutions
Singular elliptic equation

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.3934/mine.2020032

Cite this

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abstract = "The purpose of this note is to present a {"}new{"} approach to the decay rate of the solutions to the no-sign obstacle problem from the free boundary, based on Weiss-monotonicity formula. In presenting the approach we have chosen to treat a problem which is not touched earlier in the existing literature. Although earlier techniques may still work for this problem, we believe this approach gives a shorter proof, and may have wider applications.",

keywords = "No-sign obstacle problem, Regularity of solutions, Singular elliptic equation",

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AU - Minne, Andreas

AU - Shahgholian, Henrik

AU - Weiss, Georg S.

PY - 2020

Y1 - 2020

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AB - The purpose of this note is to present a "new" approach to the decay rate of the solutions to the no-sign obstacle problem from the free boundary, based on Weiss-monotonicity formula. In presenting the approach we have chosen to treat a problem which is not touched earlier in the existing literature. Although earlier techniques may still work for this problem, we believe this approach gives a shorter proof, and may have wider applications.

KW - No-sign obstacle problem

KW - Regularity of solutions

KW - Singular elliptic equation

UR - https://www.scopus.com/pages/publications/85104234990

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DO - 10.3934/mine.2020032

M3 - Article

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IS - 4

ER -

Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type

Abstract

Keywords

ASJC Scopus subject areas

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