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Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints

This paper is concerned with the existence and regularity of minimizers to an optimal control problem governed by semilinear elliptic equations, in which mixed pointwise control-state constraints are considered in a quite general form and the controls act simultaneously in the domain and on the boun...

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Main Authors:	V, H.Nhu, N, Q.Tuan, N, B.Giang, N,T.T.Huong
Format:	Bài trích
Language:	English
Published:	Elsevier 2022
Subjects:	Existence of optimal solution Regularity of optimal solution
Online Access:	https://www.sciencedirect.com/science/article/abs/pii/S0022247X22001536?via%3Dihub https://dlib.phenikaa-uni.edu.vn/handle/PNK/5777 https://doi.org/10.1016/j.jmaa.2022.126139
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spelling	oai:localhost:PNK-57772022-08-17T05:54:54Z Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints V, H.Nhu N, Q.Tuan N, B.Giang N,T.T.Huong Existence of optimal solution Regularity of optimal solution This paper is concerned with the existence and regularity of minimizers to an optimal control problem governed by semilinear elliptic equations, in which mixed pointwise control-state constraints are considered in a quite general form and the controls act simultaneously in the domain and on the boundary. The - and -type regularization is considered for both distributed and boundary controls. Under standing assumptions, the minimizers and the corresponding multipliers do exist. Furthermore, by applying the bootstrapping technique and using some calculation tools for functions in Sobolev spaces of fractional order, the optimal solutions are shown to be Lipschitz continuous when the -type regularization is applied and they are proven to be Hölder continuous with the exponent if only -type regularization is used. 2022-05-05T07:26:24Z 2022-05-05T07:26:24Z 2022 Bài trích https://www.sciencedirect.com/science/article/abs/pii/S0022247X22001536?via%3Dihub https://dlib.phenikaa-uni.edu.vn/handle/PNK/5777 https://doi.org/10.1016/j.jmaa.2022.126139 en Elsevier
institution	Digital Phenikaa
collection	Digital Phenikaa
language	English
topic	Existence of optimal solution Regularity of optimal solution
spellingShingle	Existence of optimal solution Regularity of optimal solution V, H.Nhu N, Q.Tuan N, B.Giang N,T.T.Huong Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints
description	This paper is concerned with the existence and regularity of minimizers to an optimal control problem governed by semilinear elliptic equations, in which mixed pointwise control-state constraints are considered in a quite general form and the controls act simultaneously in the domain and on the boundary. The - and -type regularization is considered for both distributed and boundary controls. Under standing assumptions, the minimizers and the corresponding multipliers do exist. Furthermore, by applying the bootstrapping technique and using some calculation tools for functions in Sobolev spaces of fractional order, the optimal solutions are shown to be Lipschitz continuous when the -type regularization is applied and they are proven to be Hölder continuous with the exponent if only -type regularization is used.
format	Bài trích
author	V, H.Nhu N, Q.Tuan N, B.Giang N,T.T.Huong
author_facet	V, H.Nhu N, Q.Tuan N, B.Giang N,T.T.Huong
author_sort	V, H.Nhu
title	Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints
title_short	Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints
title_full	Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints
title_fullStr	Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints
title_full_unstemmed	Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints
title_sort	continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints
publisher	Elsevier
publishDate	2022
url	https://www.sciencedirect.com/science/article/abs/pii/S0022247X22001536?via%3Dihub https://dlib.phenikaa-uni.edu.vn/handle/PNK/5777 https://doi.org/10.1016/j.jmaa.2022.126139
_version_	1751856282526023680
score	8.881002

Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints

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