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.
2010
39
1-2
101
120
https://doi.org/10.1007/s00526-009-0303-9
Gigli, Nicola
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/17392
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