Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below
By Marc Arnaudon, Anton Thalmaier, Feng-Yu Wang. 2006
128 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b8f22b0ea7b4b2d73023035af9aa3eb0417dcb4a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Arnaud Guillin
- Patrick Cattiaux
- Wei Liu
- Michael Röckner
- Feng-Yu Wang
- Nathael Gozlan
- Wei David Liu
- Liming Wu
In Mathematical Physics
- Michael Röckner
- Arnaud Guillin
- Patrick Cattiaux
- Feng-Yu Wang
- Wei Liu
- Wei David Liu
- Liming Wu
- Giuseppe Da Prato
Citations in the corpus
- Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, methodology): “The coupling we used here, which only depends on the natural distance between two marginal processes, is a modification of the argument in [3].”
- A note on Talagrand’s transportation inequality and logarithmic Sobolev inequality (2008, background): “Also see [2] for the Harnack type inequality on this type of manifold.”
- Harnack inequality and strong Feller property for stochastic fast-diffusion equations☆ (2007, methodology): “The approach used in [20] is based on a coupling argument developed in [4], where Harnack inequalities are studied for diffusion semigroups on Riemannian manifolds with unbounded below curvatures.”
- Log-Harnack Inequality for Stochastic Differential Equations in Hilbert Spaces and its Consequences (2009, methodology): “To establish this inequality for diffusions with curvature unbounded below, a coupling method is developed in [1].”
- Equivalent semigroup properties for the curvature-dimension condition (2010, unknown): “ 0. Now, let (X 0,Y 0) have distribution π such that π(˜ρp) = Wρ˜ p (µ 1,µ 2) p. Using the coupling by parallel displacement rather than by reflection, we have (see [20, Proof of Proposition 2.5.1] or [1]) dρ(Xt,Yt) ≤ IZ(Xt,Yt)dt. Combining this with (2.15) we conclude that d˜ρ(Xt,Yt) ≤ eKtρ˜(Xt,Yt).”
- Harnack inequalities for stochastic equations driven by Levy noise (2012, background): “roduced in [22] and the log-Harnack inequality introduced in [17, 25] have been intensively investigated and applied for stochastic (partial) differential equations driven by Gaussian noises, see e.g. [3, 23, 13, 4, 7, 8, 12, 24, 34, 9, 14, 29, 30, 10, 15, 31, 32, 33] and references within. Due to te”
- Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups (2008, background): “The main aim is to prove a Harnack inequality for its transition semigroup in the sense of [18] (see also [1, 16, 19] for further development) and exploit its consequences.”