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arXiv:2307.13456 [math.AP]AbstractReferencesReviewsResources

Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces

Wojciech Górny

Published 2023-07-25Version 1

We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solutions to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their existence and uniqueness and show that they are also variational solutions; in particular, this is an existence result for variational solutions. Then, we apply this technique in the case of a gradient flow of a functional with inhomogeneous growth.

Comments: 29 pages. arXiv admin note: text overlap with arXiv:2103.13373
Categories: math.AP, math.FA
Subjects: 49J52, 58J35, 35K90, 35K92
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