Global properties of invariant measures

By Giorgio Metafune, D. Pallara, Abdelaziz Rhandi. 2005

70 citations recorded by the source corpus.

Abstract We study global regularity properties of invariant measures associated with second order differential operators in R N . Under suitable conditions, we prove global boundedness of the density, Sobolev regularity, a Harnack inequality and pointwise upper and lower bounds.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/baae01cdcf3529370cb1762becf11278ac66965b

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Stationary focusing mean-field games (2016, methodology): “If one just looks at the Kolmogorov equation, integrability of the vector eld −∇H(∇u) with respect tom is recommended to ensure some minimal regularity ofm and uniqueness of the invariant distribution itself [35].”
On large deviations of coupled diffusions with time scale separation (2013, background): “The second one is a local version of the result by Bogachev, Krylov and Röckner [6] that if b ∈ L2(Rd,m(x) dx) then √ m ∈ W1,2(Rd), and is proved along similar lines; see also Metafune, Pallara and Rhandi [31].”