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On improvement of summability properties in nonautonomous Kolmogorov equations
1. | Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy |
2. | Dipartimento di Matematica, Università degli Studi di Parma, Viale Parco Area delle Scienze 53/A, I-43124 Parma |
References:
[1] |
L. Angiuli, Pointwise gradient estimates for evolution operators associated with Kolmogorov operators , Arch. Math. (Basel), 101 (2013), 159-170.
doi: 10.1007/s00013-013-0542-z. |
[2] |
L. Angiuli and L. Lorenzi, Compactness and invariance properties of evolution operators associated to Kolmogorov operators with unbounded coefficients , J. Math. Anal. Appl., 379 (2011), 125-149.
doi: 10.1016/j.jmaa.2010.12.029. |
[3] |
L. Angiuli, L. Lorenzi and A. Lunardi, Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations , Comm. Partial Differential Equations, 38 (2013), 2049-2080. |
[4] |
E. A. Carlen, S. Kusuoka and D. W. Stroock, Upper bounds for symmetric Markov transition functions , Ann. Inst. H. Poincaré Probab. Statist., 23 (1987), 245-287. |
[5] |
G. Da Prato and A. Lunardi, Ultraboundedness for parabolic equations in convex domains without boundary conditions , Phys. D, 239 (2010), 1453-1457.
doi: 10.1016/j.physd.2009.02.004. |
[6] |
E. B. Davies and B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians , J. Funct. Anal., 59 (1984), 335-395.
doi: 10.1016/0022-1236(84)90076-4. |
[7] |
E. B. Davies, Heat kernes and spectral theory, Cambridge tracts in Mathematics, 92, Cambridge Univ. Press, Cambridge, 1990.
doi: ISBN: 0-521-40997-7. |
[8] |
M. Geissert and A. Lunardi, Invariant measures and maximal $L^2$ regularity for nonautonomous Ornstein-Uhlenbeck equations , J. Lond. Math. Soc. (2), 77 (2008), 719-740.
doi: 10.1112/jlms/jdn009. |
[9] |
L. Gross, Logarithmic Sobolev inequalities , Amer. J. Math., 97 (1975), 1061-1083.
doi: 10.2307/2373688. |
[10] |
O. Kavian, G. Kerkyacharian and B. Roynette, Quelques remarques sur l'ultracontractivité, J. Funct. Anal., 11 (1993), 155-196.
doi: 10.1006/jfan.1993.1008. |
[11] |
M. Kunze, L. Lorenzi and A. Lunardi, Nonautonomous Kolmogorov parabolic equations with unbounded coefficients , Trans. Amer. Math. Soc., 362 (2010), 169-198.
doi: 10.1090/S0002-9947-09-04738-2. |
[12] |
M. Ledoux, Remarks on Logarithmic Sobolev constants, exponential integrability, and bounds on the diameter , J. Math. Kyoto Univ., 35 (1995), 211-220. |
[13] |
A. Lunardi, Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in $\mathbb{R}^{d}$ , in Parabolic Problems. The Herbert Amann Festschrift, Progress in Nonlinear Differential Equations and Their Applications, 80, Birkhäuser, Basel, 2011.
doi: 10.1007/978-3-0348-0075-4_23. |
[14] |
P. Maheux, New proofs of Davies-Simon's theorems about ultracontractivity and Logarithmic Sobolev inequalities related to Nash type inequalities , Available on arXiv (http://arxiv.org/abs/0609124v1), (2006). |
[15] |
E. Nelson, The free Markoff field , J. Funct. Anal., 12 (1973), 211-227.
doi: 10.1016/0022-1236(73)90025-6. |
[16] |
M. Röckner and F.-Y. Wang, Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds , Forum Math., 15 (2003), 893-921.
doi: 10.1515/form.2003.044. |
[17] |
F.-Y. Wang, Logarithmic Sobolev inequalities on noncompact Riemann manifolds , Probab. Theory Relat. Fields, 109 (1997), 417-434.
doi: 10.1007/s004400050137. |
[18] |
F.-Y. Wang, Functional inequalities for empty essential spectrum , J. Funct. Anal., 170 (2000), 219-245.
doi: 10.1006/jfan.1999.3516. |
[19] |
F.-Y. Wang, A character of the gradient estimate for diffusion semigroups , Proc. Amer. Math. Soc., 133 (2004), 827-834.
doi: 10.1090/S0002-9939-04-07625-7. |
[20] |
F.-Y. Wang, Functional inequalities in Markov Semigroups and Spectral Theory, Science Press, Beijing, 2004.
doi: ISBN: 978-0-08-044942-5. |
show all references
References:
[1] |
L. Angiuli, Pointwise gradient estimates for evolution operators associated with Kolmogorov operators , Arch. Math. (Basel), 101 (2013), 159-170.
doi: 10.1007/s00013-013-0542-z. |
[2] |
L. Angiuli and L. Lorenzi, Compactness and invariance properties of evolution operators associated to Kolmogorov operators with unbounded coefficients , J. Math. Anal. Appl., 379 (2011), 125-149.
doi: 10.1016/j.jmaa.2010.12.029. |
[3] |
L. Angiuli, L. Lorenzi and A. Lunardi, Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations , Comm. Partial Differential Equations, 38 (2013), 2049-2080. |
[4] |
E. A. Carlen, S. Kusuoka and D. W. Stroock, Upper bounds for symmetric Markov transition functions , Ann. Inst. H. Poincaré Probab. Statist., 23 (1987), 245-287. |
[5] |
G. Da Prato and A. Lunardi, Ultraboundedness for parabolic equations in convex domains without boundary conditions , Phys. D, 239 (2010), 1453-1457.
doi: 10.1016/j.physd.2009.02.004. |
[6] |
E. B. Davies and B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians , J. Funct. Anal., 59 (1984), 335-395.
doi: 10.1016/0022-1236(84)90076-4. |
[7] |
E. B. Davies, Heat kernes and spectral theory, Cambridge tracts in Mathematics, 92, Cambridge Univ. Press, Cambridge, 1990.
doi: ISBN: 0-521-40997-7. |
[8] |
M. Geissert and A. Lunardi, Invariant measures and maximal $L^2$ regularity for nonautonomous Ornstein-Uhlenbeck equations , J. Lond. Math. Soc. (2), 77 (2008), 719-740.
doi: 10.1112/jlms/jdn009. |
[9] |
L. Gross, Logarithmic Sobolev inequalities , Amer. J. Math., 97 (1975), 1061-1083.
doi: 10.2307/2373688. |
[10] |
O. Kavian, G. Kerkyacharian and B. Roynette, Quelques remarques sur l'ultracontractivité, J. Funct. Anal., 11 (1993), 155-196.
doi: 10.1006/jfan.1993.1008. |
[11] |
M. Kunze, L. Lorenzi and A. Lunardi, Nonautonomous Kolmogorov parabolic equations with unbounded coefficients , Trans. Amer. Math. Soc., 362 (2010), 169-198.
doi: 10.1090/S0002-9947-09-04738-2. |
[12] |
M. Ledoux, Remarks on Logarithmic Sobolev constants, exponential integrability, and bounds on the diameter , J. Math. Kyoto Univ., 35 (1995), 211-220. |
[13] |
A. Lunardi, Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in $\mathbb{R}^{d}$ , in Parabolic Problems. The Herbert Amann Festschrift, Progress in Nonlinear Differential Equations and Their Applications, 80, Birkhäuser, Basel, 2011.
doi: 10.1007/978-3-0348-0075-4_23. |
[14] |
P. Maheux, New proofs of Davies-Simon's theorems about ultracontractivity and Logarithmic Sobolev inequalities related to Nash type inequalities , Available on arXiv (http://arxiv.org/abs/0609124v1), (2006). |
[15] |
E. Nelson, The free Markoff field , J. Funct. Anal., 12 (1973), 211-227.
doi: 10.1016/0022-1236(73)90025-6. |
[16] |
M. Röckner and F.-Y. Wang, Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds , Forum Math., 15 (2003), 893-921.
doi: 10.1515/form.2003.044. |
[17] |
F.-Y. Wang, Logarithmic Sobolev inequalities on noncompact Riemann manifolds , Probab. Theory Relat. Fields, 109 (1997), 417-434.
doi: 10.1007/s004400050137. |
[18] |
F.-Y. Wang, Functional inequalities for empty essential spectrum , J. Funct. Anal., 170 (2000), 219-245.
doi: 10.1006/jfan.1999.3516. |
[19] |
F.-Y. Wang, A character of the gradient estimate for diffusion semigroups , Proc. Amer. Math. Soc., 133 (2004), 827-834.
doi: 10.1090/S0002-9939-04-07625-7. |
[20] |
F.-Y. Wang, Functional inequalities in Markov Semigroups and Spectral Theory, Science Press, Beijing, 2004.
doi: ISBN: 978-0-08-044942-5. |
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