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arXiv · 1609.02743

Variational methods for the selection of solutions to an implicit system of PDEs

Gisella Croce·Giovanni Pisante
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Abstract

We consider the vectorial system \[ \begin{cases} Du \in \mathcal{O}(2), & \mbox{a.e. in}\;\Omega, u=0, & \mbox{on} \;\partial \Omega, \end{cases} \] where $\Omega$ is a subset of $\R^2$, $u:\Omega\to \R^2$ and $\mathcal{O}(2)$ is the orthogonal group of $\R^2$. We provide a variational method to select, among the infinitely many solutions, the ones that minimize an appropriate weighted measure of the singular set of the gradient.

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Gisella Croce, Giovanni Pisante. 2016-09-09. Variational methods for the selection of solutions to an implicit system of PDEs. https://arxiv.org/abs/1609.02743

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