A differential inclusion : the case of an isotropic set
ESAIM: Control, Optimisation and Calculus of Variations (2005)
- Volume: 11, Issue: 1, page 122-138
- ISSN: 1292-8119
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topCroce, Gisella. "A differential inclusion : the case of an isotropic set." ESAIM: Control, Optimisation and Calculus of Variations 11.1 (2005): 122-138. <http://eudml.org/doc/245592>.
@article{Croce2005,
abstract = {In this article we are interested in the following problem: to find a map $u: \Omega \rightarrow \mathbb \{R\}^2$ that satisfies\[ \left\lbrace \begin\{array\}\{ll\} D u \in E\,\, &\mbox\{\{\it a.e.\} in \} \Omega \vspace\{2.84544pt\}\\ u(x)=\varphi (x) &x \in \partial \Omega \hspace\{85.35826pt\} \end\{array\} \right. \]where $\Omega $ is an open set of $\mathbb \{R\}^2$ and $E$ is a compact isotropic set of $\mathbb \{R\}^\{2\times 2\}$. We will show an existence theorem under suitable hypotheses on $\varphi $.},
author = {Croce, Gisella},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {rank one convex hull; polyconvex hull; differential inclusion; isotropic set; differential inclusions; boundary value problem},
language = {eng},
number = {1},
pages = {122-138},
publisher = {EDP-Sciences},
title = {A differential inclusion : the case of an isotropic set},
url = {http://eudml.org/doc/245592},
volume = {11},
year = {2005},
}
TY - JOUR
AU - Croce, Gisella
TI - A differential inclusion : the case of an isotropic set
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2005
PB - EDP-Sciences
VL - 11
IS - 1
SP - 122
EP - 138
AB - In this article we are interested in the following problem: to find a map $u: \Omega \rightarrow \mathbb {R}^2$ that satisfies\[ \left\lbrace \begin{array}{ll} D u \in E\,\, &\mbox{{\it a.e.} in } \Omega \vspace{2.84544pt}\\ u(x)=\varphi (x) &x \in \partial \Omega \hspace{85.35826pt} \end{array} \right. \]where $\Omega $ is an open set of $\mathbb {R}^2$ and $E$ is a compact isotropic set of $\mathbb {R}^{2\times 2}$. We will show an existence theorem under suitable hypotheses on $\varphi $.
LA - eng
KW - rank one convex hull; polyconvex hull; differential inclusion; isotropic set; differential inclusions; boundary value problem
UR - http://eudml.org/doc/245592
ER -
References
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- [9] R.T. Rockafellar, Convex analysis. Princeton Landmarks in Mathematics. Princeton University Press, Princeton, NJ (1997). Reprint of the 1970 original, Princeton Paperbacks. Zbl0932.90001MR1451876
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