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
Journal	Fractional Calculus and Applied Analysis
DOIs	https://doi.org/10.1007/s13540-024-00318-9
Publication status	Accepted/In press - 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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year = "2024",

doi = "10.1007/s13540-024-00318-9",

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AU - Mikayelyan, Hayk

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PY - 2024

Y1 - 2024

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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DO - 10.1007/s13540-024-00318-9

M3 - Article

AN - SCOPUS:85200649749

SN - 1311-0454

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

ER -

Optimization of the shape for a non-local control problem

Abstract

Keywords

ASJC Scopus subject areas

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