Preprint 11/2003

Parabolic systems with nowhere smooth solutions

Stefan Müller, Marc Oliver Rieger, and Vladimír Šverák

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Submission date: 08. Feb. 2003
Pages: 26
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 formula3 parabolic systems with smooth initial data and formula5 right hand side which admit solutions that are nowhere formula7. The elliptic part is in variational form and the corresponding energy formula9 is strongly quasiconvex and in particular satisfies a uniform Legendre-Hadamard (or strong ellipticity) condition.

04.01.2023, 02:12