On the heat flow on metric measure spaces: existence, uniqueness and stability

Gigli, Nicola
September 2010
Calculus of Variations & Partial Differential Equations;Sep2010, Vol. 39 Issue 1/2, p101
Academic Journal
We prove existence and uniqueness of the gradient flow of the Entropy functional under the only assumption that the functional is λ-geodesically convex for some $${\lambda\in\mathbb {R}}$$. Also, we prove a general stability result for gradient flows of geodesically convex functionals which Γ−converge to some limit functional. The stability result applies directly to the case of the Entropy functionals on compact spaces.


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