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Asymptotic analysis of a spatially and size-structured population model with delayed birth process
Some observations on the Green function for the ball in the fractional Laplace framework
1. | Dipartimento di Matematica "Federigo Enriques", Università degli Studi di Milano, Via Cesare Saldini, 50, I-20133, Milano, Italy |
References:
[1] |
Milton Abramowitz and Irene Anne Stegun eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York; National Bureau of Standards, Washington, DC, 1984. |
[2] |
R. M. Blumenthal, R. K. Getoor and D. B. Ray, On the distribution of first hits for the symmetric stable processes, Trans. Amer. Math. Soc., 99 (1961), 540-554. |
[3] |
Claudia Bucur and Enrico Valdinoci, Nonlocal diffusion and applications, accepted for Publication for the Springer Series Lecture Notes of the Unione Matematica Italiana, preprint arXiv:1504.08292, 2015. |
[4] |
Eleonora Di Nezza, Giampiero Palatucci and Enrico Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., 136 (2012), 521-573.
doi: 10.1016/j.bulsci.2011.12.004. |
[5] |
Bartłomiej Dyda, Fractional Hardy inequality with a remainder term, Colloq. Math., 122 (2011), 59-67.
doi: 10.4064/cm122-1-6. |
[6] |
Bartłomiej Dyda, Fractional calculus for power functions and eigenvalues of the fractional Laplacian, Fract. Calc. Appl. Anal., 15 (2012), 536-555.
doi: 10.2478/s13540-012-0038-8. |
[7] |
Lawrence C. Evans, Partial Differential Equations, volume 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, second edition, 2010.
doi: 10.1090/gsm/019. |
[8] |
Yitzhak Katznelson, An Introduction to Harmonic Analysis, Cambridge Mathematical Library. Cambridge University Press, Cambridge, third edition, 2004.
doi: 10.1017/CBO9781139165372. |
[9] |
Tadeusz Kulczycki, Properties of Green function of symmetric stable processes, Probab. Math. Statist., 17 (1997), 339-364. |
[10] |
N. S. Landkof, Foundations of Modern Potential Theory, Springer-Verlag, New York-Heidelberg, 1972. Translated from the Russian by A. P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften, Band 180. |
[11] |
Michael Reed and Barry Simon, Methods of Modern Mathematical Physics. I. Functional Analysis, Academic Press, New York-London, 1972. |
[12] |
Luis Silvestre, Regularity of the obstacle problem for a fractional power of the Laplace operator, Comm. Pure Appl. Math., 60 (2007), 67-112.
doi: 10.1002/cpa.20153. |
[13] |
Richard L. Wheeden and Antoni Zygmund, Measure and Integral, An introduction to real analysis, Pure and Applied Mathematics, Vol. 43, Marcel Dekker, Inc., New York-Basel, 1977. |
show all references
References:
[1] |
Milton Abramowitz and Irene Anne Stegun eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York; National Bureau of Standards, Washington, DC, 1984. |
[2] |
R. M. Blumenthal, R. K. Getoor and D. B. Ray, On the distribution of first hits for the symmetric stable processes, Trans. Amer. Math. Soc., 99 (1961), 540-554. |
[3] |
Claudia Bucur and Enrico Valdinoci, Nonlocal diffusion and applications, accepted for Publication for the Springer Series Lecture Notes of the Unione Matematica Italiana, preprint arXiv:1504.08292, 2015. |
[4] |
Eleonora Di Nezza, Giampiero Palatucci and Enrico Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., 136 (2012), 521-573.
doi: 10.1016/j.bulsci.2011.12.004. |
[5] |
Bartłomiej Dyda, Fractional Hardy inequality with a remainder term, Colloq. Math., 122 (2011), 59-67.
doi: 10.4064/cm122-1-6. |
[6] |
Bartłomiej Dyda, Fractional calculus for power functions and eigenvalues of the fractional Laplacian, Fract. Calc. Appl. Anal., 15 (2012), 536-555.
doi: 10.2478/s13540-012-0038-8. |
[7] |
Lawrence C. Evans, Partial Differential Equations, volume 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, second edition, 2010.
doi: 10.1090/gsm/019. |
[8] |
Yitzhak Katznelson, An Introduction to Harmonic Analysis, Cambridge Mathematical Library. Cambridge University Press, Cambridge, third edition, 2004.
doi: 10.1017/CBO9781139165372. |
[9] |
Tadeusz Kulczycki, Properties of Green function of symmetric stable processes, Probab. Math. Statist., 17 (1997), 339-364. |
[10] |
N. S. Landkof, Foundations of Modern Potential Theory, Springer-Verlag, New York-Heidelberg, 1972. Translated from the Russian by A. P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften, Band 180. |
[11] |
Michael Reed and Barry Simon, Methods of Modern Mathematical Physics. I. Functional Analysis, Academic Press, New York-London, 1972. |
[12] |
Luis Silvestre, Regularity of the obstacle problem for a fractional power of the Laplace operator, Comm. Pure Appl. Math., 60 (2007), 67-112.
doi: 10.1002/cpa.20153. |
[13] |
Richard L. Wheeden and Antoni Zygmund, Measure and Integral, An introduction to real analysis, Pure and Applied Mathematics, Vol. 43, Marcel Dekker, Inc., New York-Basel, 1977. |
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