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Mixed norms, functional Inequalities, and Hamilton-Jacobi equations
1. | Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy, Italy |
2. | Dipartimento di Scienze di Base e Applicate, per l'Ingegneria-Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma |
References:
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A. Avantaggiati and P. Loreti, Hypercontractivity, Hopf-Lax type formulas, Ornstein-Uhlenbeck operators. II, Discrete Contin. Dyn. Syst. Ser. S, 2 (2009), 525-545.
doi: 10.3934/dcdss.2009.2.525. |
[2] |
A. Avantaggiati, P. Loreti and C. Pocci, On a class of Hamilton-Jacobi equations with related logarithmic Sobolev inequality, and optimality, Commun. Appl. Ind. Math., 2 (2011), 1-16.
doi: 10.1685/journal.caim.389. |
[3] |
A. Benedek and R. Panzone, The space $L^p$, with mixed norm, Duke Math. J., 28 (1961), 301-324.
doi: 10.1215/S0012-7094-61-02828-9. |
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S. G. Bobkov, I. Gentil and M. Ledoux, Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pures Appl. (9), 80 (2001), 669-696.
doi: 10.1016/S0021-7824(01)01208-9. |
[5] |
S. G. Bobkov and F. Götze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal., 163 (1999), 1-28.
doi: 10.1006/jfan.1998.3326. |
[6] |
I. Gentil, Ultracontractive bounds on Hamilton-Jacobi solutions, Bull. Sci. Math., 126 (2002), 507-524.
doi: 10.1016/S0007-4497(02)01128-4. |
[7] |
L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math., 97 (1975), 1061-1083.
doi: 10.2307/2373688. |
[8] |
H.-J. Schmeisser and H. Triebel, Topics in Fourier Analysis and Function Spaces, A Wiley-Interscience Publication, John Wiley & Sons Ltd., Chichester, 1987. |
show all references
References:
[1] |
A. Avantaggiati and P. Loreti, Hypercontractivity, Hopf-Lax type formulas, Ornstein-Uhlenbeck operators. II, Discrete Contin. Dyn. Syst. Ser. S, 2 (2009), 525-545.
doi: 10.3934/dcdss.2009.2.525. |
[2] |
A. Avantaggiati, P. Loreti and C. Pocci, On a class of Hamilton-Jacobi equations with related logarithmic Sobolev inequality, and optimality, Commun. Appl. Ind. Math., 2 (2011), 1-16.
doi: 10.1685/journal.caim.389. |
[3] |
A. Benedek and R. Panzone, The space $L^p$, with mixed norm, Duke Math. J., 28 (1961), 301-324.
doi: 10.1215/S0012-7094-61-02828-9. |
[4] |
S. G. Bobkov, I. Gentil and M. Ledoux, Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pures Appl. (9), 80 (2001), 669-696.
doi: 10.1016/S0021-7824(01)01208-9. |
[5] |
S. G. Bobkov and F. Götze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal., 163 (1999), 1-28.
doi: 10.1006/jfan.1998.3326. |
[6] |
I. Gentil, Ultracontractive bounds on Hamilton-Jacobi solutions, Bull. Sci. Math., 126 (2002), 507-524.
doi: 10.1016/S0007-4497(02)01128-4. |
[7] |
L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math., 97 (1975), 1061-1083.
doi: 10.2307/2373688. |
[8] |
H.-J. Schmeisser and H. Triebel, Topics in Fourier Analysis and Function Spaces, A Wiley-Interscience Publication, John Wiley & Sons Ltd., Chichester, 1987. |
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