On the existence of weak optimal BV-controls in coefficients for linear elliptic problems

In this paper we study the optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. We adopt a weight coefficient in the main part of elliptic operator as control in <em>BV(Ω). </em>Since the equations of this type can exhibit the Lavren...

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Main Authors:	I. G. Balanenko, P. I. Kogut
Format:	Article
Language:	English
Published:	DNU 2009-08-01
Series:	Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ
Subjects:	optimal control problem degenerate elliptic equation mixed boundary conditions Lavrentieff phenomenon weak admissible solutions
Online Access:	http://model-dnu.dp.ua/index.php/SM/article/view/87

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spelling	doaj-6243461a13e242e6998b231e4c03a2f22020-11-24T22:49:12ZengDNUVìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ2312-45472415-73252009-08-011789310310.15421/14090887On the existence of weak optimal BV-controls in coefficients for linear elliptic problemsI. G. Balanenko0P. I. Kogut1Днепропетровский национальный университет имени Олеся ГончараДнепропетровский национальный университет имени Олеся ГончараIn this paper we study the optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. We adopt a weight coefficient in the main part of elliptic operator as control in <em>BV(Ω). </em>Since the equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, we show that this optimal control problem is regular. Using the direct method in the Calculus of variations, we discuss the solvability of the above optimal control problems in the class of weak admissible solutions.http://model-dnu.dp.ua/index.php/SM/article/view/87optimal control problemdegenerate elliptic equationmixed boundary conditionsLavrentieff phenomenonweak admissible solutions
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	I. G. Balanenko P. I. Kogut
spellingShingle	I. G. Balanenko P. I. Kogut On the existence of weak optimal BV-controls in coefficients for linear elliptic problems Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ optimal control problem degenerate elliptic equation mixed boundary conditions Lavrentieff phenomenon weak admissible solutions
author_facet	I. G. Balanenko P. I. Kogut
author_sort	I. G. Balanenko
title	On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_short	On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_full	On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_fullStr	On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_full_unstemmed	On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_sort	on the existence of weak optimal bv-controls in coefficients for linear elliptic problems
publisher	DNU
series	Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ
issn	2312-4547 2415-7325
publishDate	2009-08-01
description	In this paper we study the optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. We adopt a weight coefficient in the main part of elliptic operator as control in <em>BV(Ω). </em>Since the equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, we show that this optimal control problem is regular. Using the direct method in the Calculus of variations, we discuss the solvability of the above optimal control problems in the class of weak admissible solutions.
topic	optimal control problem degenerate elliptic equation mixed boundary conditions Lavrentieff phenomenon weak admissible solutions
url	http://model-dnu.dp.ua/index.php/SM/article/view/87
work_keys_str_mv	AT igbalanenko ontheexistenceofweakoptimalbvcontrolsincoefficientsforlinearellipticproblems AT pikogut ontheexistenceofweakoptimalbvcontrolsincoefficientsforlinearellipticproblems
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On the existence of weak optimal BV-controls in coefficients for linear elliptic problems

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