Publication: Non-uniqueness of minimizers for strictly polyconvex functionals
Non-uniqueness of minimizers for strictly polyconvex functionals
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Spadaro, E. N. (2009). Non-uniqueness of minimizers for strictly polyconvex functionals. Archiv for Rational Mechanics and Analysis, 193(3), 659–678. https://doi.org/10.1007/s00205-008-0156-y
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In this note we solve a problem posed by Ball (in Philos Trans R Soc Lond Ser A 306(1496):557–611, 1982) about the uniqueness of smooth equilibrium solutions to boundary value problems for strictly polyconvex functionals, $$\mathcal {F}(u)=\int_\Omega f(\nabla u(x)) {\rm d}x\quad{\rm and}\quad u\vert_{\partial\Omega}=u_0,$$ where Ω is homeomorphic to a ball. We give several examples of non-uniqueness. The main example is a boundary value problem with at least two different global minimizers, both analytic up to the boundary. All these
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- Spadaro, E N
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Spadaro, E. N. (2009). Non-uniqueness of minimizers for strictly polyconvex functionals. Archiv for Rational Mechanics and Analysis, 193(3), 659–678. https://doi.org/10.1007/s00205-008-0156-y
