Non-Uniqueness of Minimizers for Strict Polyconvex Functionals

  • Emanuele Spadaro (Universität Zürich)
A3 01 (Sophus-Lie room)


In this talk we consider a problem posed by J.M. Ball about the uniqueness of smooth equilibrium solutions to boundary value problems for strictly polyconvex functionals, $$ \F(u)=\int_\Omega f(\nabla u(x))\,\dd x\quad\m{and}\quad u\vert_{\de\Omega}=u_0\,, $$ where $\Omega$ is homeomorphic to a ball.

We give several examples of non-uniqueness, the main of which is such a boundary value problem with at least two analytic different minimizers. All this examples are suggested by the theory of Minimal Surfaces.

Anne Dornfeld

MPI for Mathematics in the Sciences Contact via Mail

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