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Teor. Veroyatnost. i Primenen., 2009, Volume 54, Issue 1, Pages 116–148 (Mi tvp2549)  

This article is cited in 15 scientific papers (total in 15 papers)

Global properties of transition pProbabilities of singular diffusions

G. Metafunea, D. Pallaraa, A. Rhandib

a Lecce University
b University of Salerno

Abstract: We prove global Sobolev regularity and pointwise upper bounds for transition densities associated with second order differential operators in $R^N$ with unbounded drift. As an application, we obtain sufficient conditions implying the differentiability of the associated transition semigroup on the space of bounded and continuous functions on $R^N$.

Keywords: transition semigroups, transition probabilities, parabolic regularity

DOI: https://doi.org/10.4213/tvp2549

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English version:
Theory of Probability and its Applications, 2010, 54:1, 68–96

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Received: 28.03.2008

Citation: G. Metafune, D. Pallara, A. Rhandi, “Global properties of transition pProbabilities of singular diffusions”, Teor. Veroyatnost. i Primenen., 54:1 (2009), 116–148; Theory Probab. Appl., 54:1 (2010), 68–96

Citation in format AMSBIB
\by G.~Metafune, D.~Pallara, A.~Rhandi
\paper Global properties of transition pProbabilities of singular diffusions
\jour Teor. Veroyatnost. i Primenen.
\yr 2009
\vol 54
\issue 1
\pages 116--148
\jour Theory Probab. Appl.
\yr 2010
\vol 54
\issue 1
\pages 68--96

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    This publication is cited in the following articles:
    1. V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Russian Math. Surveys, 64:6 (2009), 973–1078  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. Fornaro S., Fusco N., Metafune G., Pallara D., “Sharp upper bounds for the density of some invariant measures”, Proc. Roy. Soc. Edinburgh Sect. A, 139:6 (2009), 1145–1161  crossref  mathscinet  zmath  isi  elib  scopus
    3. Shaposhnikov S.V., “Lower estimates for densities of solutions to parabolic equations for measures”, Dokl. Math., 80:3 (2009), 877–881  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. Shaposhnikov S.V., “Estimates of solutions of parabolic equations for measures”, Dokl. Math., 82:2 (2010), 769–772  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. Aibeche A., Laidoune K., Rhandi A., “Time dependent Lyapunov functions for some Kolmogorov semigroups perturbed by unbounded potentials”, Arch. Math. (Basel), 94:6 (2010), 565–577  crossref  mathscinet  zmath  isi  scopus
    6. Metafune G., Ouhabaz E.M., Pallara D., “Long time behavior of heat kernels of operators with unbounded drift terms”, J. Math. Anal. Appl., 377:1 (2011), 170–179  crossref  mathscinet  zmath  isi  elib  scopus
    7. S. V. Shaposhnikov, “Regular and qualitative properties of solutions for parabolic equations for measures”, Theory Probab. Appl., 56:2 (2011), 252–279  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. S. V. Shaposhnikov, “On the uniqueness of a probabilistic solution of the Cauchy problem for the Fokker–Planck–Kolmogorov equation”, Theory Probab. Appl., 56:1 (2012), 96–115  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Goldstein G.R., Goldstein J.A., Rhandi A., “Weighted Hardy's inequality and the Kolmogorov equation perturbed by an inverse-square potential”, Appl. Anal., 91:11 (2012), 2057–2071  crossref  mathscinet  zmath  isi  scopus
    10. S. V. Shaposhnikov, “The Fokker–Planck–Kolmogorov equations with a potential and a non-uniformly elliptic diffusion matrix”, Trans. Moscow Math. Soc., 74 (2013), 15–29  mathnet  crossref  mathscinet  zmath  elib
    11. Kunze M. Lorenzi L. Rhandi A., “Kernel estimates for nonautonomous Kolmogorov equations”, Adv. Math., 287 (2016), 600–639  crossref  mathscinet  zmath  isi  elib  scopus
    12. Cirant M., Tonon D., “Time-Dependent Focusing Mean-Field Games: the Sub-Critical Case”, J. Dyn. Differ. Equ., 31:1 (2019), 49–79  crossref  mathscinet  zmath  isi  scopus
    13. Camilli F., Goffi A., “Existence and Regularity Results For Viscous Hamilton-Jacobi Equations With Caputo Time-Fractional Derivative”, NoDea-Nonlinear Differ. Equ. Appl., 27:2 (2020), 22  crossref  mathscinet  isi
    14. Cirant M., Goffi A., “Lipschitz Regularity For Viscous Hamilton-Jacobi Equations With l-P Terms”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 37:4 (2020), 757–784  crossref  mathscinet  isi
    15. Bogachev I V. Shaposhnikov V S., “Representations of Solutions to Fokker-Planck-Kolmogorov Equations With Coefficients of Low Regularity”, J. Evol. Equ., 20:2 (2020), 355–374  crossref  mathscinet  isi
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