On the heat flow on metric measure spaces: existence, uniqueness and stability.(English)Zbl 1200.35178
Summary: We prove existence and uniqueness of the gradient flow of the entropy functional under the only assumption that the functional is \(\lambda \)-geodesically convex for some \(\lambda\in\mathbb R\). Also, we prove a general stability result for gradient flows of geodesically convex functionals which \(\Gamma \)-converge to some limit functional. The stability result applies directly to the case of the entropy functionals on compact spaces.
MSC:
| 35K90 | Abstract parabolic equations |
| 60B05 | Probability measures on topological spaces |
| 28A33 | Spaces of measures, convergence of measures |
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
| 35B35 | Stability in context of PDEs |
Cite
Full Text:DOI
References:
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