Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces
Analysis of PDEs
2023-07-26 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2307.13456,
title = {Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces},
author = {Wojciech Górny},
journal= {arXiv preprint arXiv:2307.13456},
year = {2023}
}
Comments
29 pages. arXiv admin note: text overlap with arXiv:2103.13373