Optimization of the shape for a non-local control problem

Zhiwei Cheng; Hayk Mikayelyan

doi:10.1007/s13540-024-00318-9

Optimization of the shape for a non-local control problem

Zhiwei Cheng, Hayk Mikayelyan

School of Mathematical Sciences

Research output: Journal Publication › Article › peer-review

Abstract

The paper studies the fractional order version of the reinforced membrane problem introduced in [A. Henrot and H. Maillot, 2001]. Existence and uniqueness of the solutions of the corresponding non-local equations has been proven for the relaxed problem. In addition, for the radial symmetric case the existence of the optimal domain has been shown.

Original language	English
Pages (from-to)	2482-2501
Number of pages	20
Journal	Fractional Calculus and Applied Analysis
Volume	27
Issue number	5
DOIs	https://doi.org/10.1007/s13540-024-00318-9
Publication status	Published - Oct 2024

Keywords

35J61
35R11
Fractional Laplacian
Optimal rearrangement
Shape optimization

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s13540-024-00318-9

Cite this

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title = "Optimization of the shape for a non-local control problem",

abstract = "The paper studies the fractional order version of the reinforced membrane problem introduced in [A. Henrot and H. Maillot, 2001]. Existence and uniqueness of the solutions of the corresponding non-local equations has been proven for the relaxed problem. In addition, for the radial symmetric case the existence of the optimal domain has been shown.",

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author = "Zhiwei Cheng and Hayk Mikayelyan",

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AU - Mikayelyan, Hayk

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Y1 - 2024/10

N2 - The paper studies the fractional order version of the reinforced membrane problem introduced in [A. Henrot and H. Maillot, 2001]. Existence and uniqueness of the solutions of the corresponding non-local equations has been proven for the relaxed problem. In addition, for the radial symmetric case the existence of the optimal domain has been shown.

AB - The paper studies the fractional order version of the reinforced membrane problem introduced in [A. Henrot and H. Maillot, 2001]. Existence and uniqueness of the solutions of the corresponding non-local equations has been proven for the relaxed problem. In addition, for the radial symmetric case the existence of the optimal domain has been shown.

KW - 35J61

KW - 35R11

KW - Fractional Laplacian

KW - Optimal rearrangement

KW - Shape optimization

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JO - Fractional Calculus and Applied Analysis

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ER -

Optimization of the shape for a non-local control problem

Abstract

Keywords

ASJC Scopus subject areas

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