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Parabolic Systems with Nowhere Smooth Solutions |
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| Authors: | |
| Institution: | (1) Max Planck Institute for Mathematics in the Sciences, Inselstr 22-26, 04103 Leipzig, Germany;(2) Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy;(3) Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA |
| Abstract: | We construct smooth 2×2 parabolic systems with smooth initial data and Cα right-hand side which admit solutions that are nowhere C1. The elliptic part is in variational form and the corresponding energy ϕ is strongly quasiconvex and in particular satisfies a uniform Legendre-Hadamard (or strong ellipticity) condition. |
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