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research article
Integral Convexity And Parabolic Systems
January 1, 2020
In this work we give optimal, i.e., necessary and sufficient, conditions for integrals of the calculus of variations to guarantee the existence of solutions-both weak and variational solutions-to the associated L-2-gradient flow. The initial values are merely L-2 functions with possibly infinite energy. In this context, the notion of integral convexity, i.e., the convexity of the variational integral and not of the integrand, plays the crucial role; surprisingly, this type of convexity is weaker than the convexity of the integrand. We demonstrate this by means of certain quasi-convex and nonconvex integrands.
Type
research article
Web of Science ID
WOS:000546971100017
Authors
Publication date
2020-01-01
Publisher
Published in
Volume
52
Issue
2
Start page
1489
End page
1525
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
July 23, 2020
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