We prove existence and uniqueness of the gradient flow of the Entropy functional under the only assumption that the functional is k-geodesically convex for some real number k . 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.
On the heat flow on metric measure spaces: Existence, uniqueness and stability / Gigli, Nicola. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 39:1-2(2010), pp. 101-120. [10.1007/s00526-009-0303-9]
On the heat flow on metric measure spaces: Existence, uniqueness and stability
Gigli, Nicola
2010-01-01
Abstract
We prove existence and uniqueness of the gradient flow of the Entropy functional under the only assumption that the functional is k-geodesically convex for some real number k . 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.| File | Dimensione | Formato | |
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