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MiS Preprint
11/2003

Parabolic systems with nowhere smooth solutions

Stefan Müller, Marc Oliver Rieger and Vladimír Šverák

Abstract

We construct smooth $2\times 2$ parabolic systems with smooth initial data and $C^\alpha$ right hand side which admit solutions that are nowhere $C^1$. The elliptic part is in variational form and the corresponding energy $\phi$ is strongly quasiconvex and in particular satisfies a uniform Legendre-Hadamard (or strong ellipticity) condition.

Received:
Feb 8, 2003
Published:
Feb 8, 2003
MSC Codes:
35B65, 35K55
Keywords:
regularity, parabolic systems, convex integration

Related publications

inJournal
2005 Repository Open Access
Stefan Müller, Marc Oliver Rieger and Vladimír Šverák

Parabolic systems with nowhere smooth solutions

In: Archive for rational mechanics and analysis, 177 (2005) 1, pp. 1-20