Parabolic Systems with Nowhere Smooth Solutions
Stefan Müller
Max Planck Institute for Mathematics in the Sciences
Ineselstr 22-26
04103 Leipzig, Germany
sm@mis.mpg.de
Marc Oliver Rieger
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rieger@sns.it
Vladimir Sverak
Department of Mathematics
University of Minnesota
Minneapolis, MN 55455
sverak@math.umn.edu
Abstract
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 energh
is strongly quasiconvex and n particular satisfies a
uniform Legendre-Hdamard (or sttrong ellipticity) condition.
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