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On Henig Regularization of Material Design Problems for Quasi-Linear <i>p</i>-Biharmonic Equation
Department of Differential Equations, Dnipropetrovsk National University, Dnipro, Ukraine
Department Mathematik, Lehrstuhl II Universität Erlangen-Nürnberg Cauerstr, Erlangen, Germany
Department Mathematik, Lehrstuhl II Universität Erlangen-Nürnberg Cauerstr, Erlangen, Germany
- 1 Department of Differential Equations, Dnipropetrovsk National University, Dnipro, Ukraine
- 2 Department Mathematik, Lehrstuhl II Universität Erlangen-Nürnberg Cauerstr, Erlangen, Germany
- 3 Department Mathematik, Lehrstuhl II Universität Erlangen-Nürnberg Cauerstr, Erlangen, Germany
Applied Mathematics·Volume 07 (2016)·Pages 1547–1570·Published 17 August 2016·DOI10.4236/am.2016.714134
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Abstract
We study a Dirichlet optimal design problem for a quasi-linear monotone p-biharmonic equation with control and state constraints. We take the coefficient of the p-biharmonic operator as a design variable in . In this article, we discuss the relaxation of such problem.
Keywords<i>p</i>-Biharmonic ProblemOptimal DesignRelaxationHenig Dilating ConeExistence Result
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