Parabolic systems with nowhere smooth solutions
Stefan Müller, Marc Oliver Rieger, and Vladimír Sverák
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Submission date: 08. Feb. 2003
published in: Archive for rational mechanics and analysis, 177 (2005) 1, p. 1-20
DOI number (of the published article): 10.1007/s00205-004-0352-3
MSC-Numbers: 35B65, 35K55
Keywords and phrases: regularity, parabolic systems, convex integration
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We construct smooth parabolic systems with smooth initial data and right hand side which admit solutions that are nowhere . The elliptic part is in variational form and the corresponding energy is strongly quasiconvex and in particular satisfies a uniform Legendre-Hadamard (or strong ellipticity) condition.