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Preface special issue: Advances and applications in qualitative studies of dynamics
Analytic semigroups and some degenerate evolution equations defined on domains with corners
1. | Dipartimento di Matematica e Fisica “E. De Giorgi", Università del Salento, Via Per Arnesano, P.O. Box 193, I-73100 Lecce, Italy |
2. | Department of Mathematics “E. De Giorgi”, University of Salento, P.O. Box 193, Via Per Arnesano, 73100 Lecce, Italy |
References:
[1] |
A. A. Albanese, M. Campiti and E. Mangino, Approximation formulas for $C_0$-semigroups and their resolvent, J. Appl. Funct. Anal., 1 (2006), 343-358. |
[2] |
A. A. Albanese, M. Campiti and E. Mangino, Regularity properties of semigroups generated by some Fleming-Viot type operators, J. Math. Anal. Appl., 335 (2007), 1259-1273.
doi: 10.1016/j.jmaa.2007.02.042. |
[3] |
A. A. Albanese and E. Mangino, A class of non-symmetric forms on the canonical simplex of $S^d$, Discrete and Continuous Dynamical Systems-Series A, 23 (2009), 639-654.
doi: 10.3934/dcds.2009.23.639. |
[4] |
A. A. Albanese and E. Mangino, Analyticity of a class of degenerate evolution equations on the simplex of $S^d$ arising from Fleming-Viot processes, J. Math. Anal. Appl., 379 (2011), 401-424.
doi: 10.1016/j.jmaa.2011.01.015. |
[5] |
A. A. Albanese and E. Mangino, One-dimensional degenerate diffusion operators, Mediterr. J. Math., 10 (2013), 707-729.
doi: 10.1007/s00009-013-0279-8. |
[6] |
S. Angenent, Local existence and regularity for a class of degenerate parabolic equations, Math. Ann., 280 (1988), 465-482.
doi: 10.1007/BF01456337. |
[7] |
S. R. Athreya, R. F. Bass and E. A. Perkins, Hölder norm estimates for elliptic operators on finite and infinite-dimensional spaces, Trans. Amer. Math. Soc., 357 (2005), 5001-5029.
doi: 10.1090/S0002-9947-05-03638-X. |
[8] |
R. F. Bass and E. A. Perkins, Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains, Trans. Amer. Math. Soc., 355 (2002), 373-405.
doi: 10.1090/S0002-9947-02-03120-3. |
[9] |
H. Brezis, W. Rosenkrants and B. Singer, On a degenerate elliptic-parabolic equation occurring in the theory of probability, Comm. Pure Appl. Math., 24 (1971), 395-416.
doi: 10.1002/cpa.3160240305. |
[10] |
M. Campiti and G. Metafune, Ventcel's boundary conditions and analytic semigroups, Arch. Math., 70 (1998), 377-390.
doi: 10.1007/s000130050210. |
[11] |
M. Campiti and I. Rasa, Qualitative properties of a class of Fleming-Viot operators, Acta Math. Hungar., 103 (2004), 55-69.
doi: 10.1023/B:AMHU.0000028236.59446.da. |
[12] |
S. Cerrai and P. Clément, On a class of degenerate elliptic operators arising from the Fleming-Viot processes, J. Evol. Equ., 1 (2001), 243-276.
doi: 10.1007/PL00001370. |
[13] |
S. Cerrai and P. Clément, Schauder estimates for a degenerate second-order elliptic operator on a cube, J. Differential Equations, 242 (2007), 287-321.
doi: 10.1016/j.jde.2007.08.002. |
[14] |
P. Clément and C. A. Timmermans, On $C_0$-semigroup generated by differential operators satisfying Ventcel's boundary conditions, Indag. Math., 89 (1986), 379-387. |
[15] |
J. R. Dorroh, Contraction semi-groups in a function space, Pacific J. Math., 19 (1966), 35-38.
doi: 10.2140/pjm.1966.19.35. |
[16] |
K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, 194, Springer, New York, Berlin, Heildelberg, 2000. |
[17] |
C. L. Epstein and R. Mazzeo, Wright-Fisher diffusion in one dimension, SIAM J. Math. Anal., 42 (2010), 1429-1436.
doi: 10.1137/090766152. |
[18] |
C. L. Epstein and R. Mazzeo, Degenerate Diffusion Operators Arising in Population Biology, Annals of Math. Studies, Princeton University Press, 2012. |
[19] |
S. N. Ethier, A class of degenerate diffusion processes occurring in population genetics, Comm. Pure Appl. Math., 29 (1976), 483-493.
doi: 10.1002/cpa.3160290503. |
[20] |
S. N. Ethier and T. G. Kurtz, Markov Processes, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, 1986.
doi: 10.1002/9780470316658. |
[21] |
S. N. Ethier and T. G. Kurtz, Fleming-Viot processes in population genetics, SIAM J. Control Optim., 31 (1993), 345-386.
doi: 10.1137/0331019. |
[22] |
W. Feller, Two singular diffusion problems, Ann. of Math., 54 (1951), 173-181.
doi: 10.2307/1969318. |
[23] |
W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math., 55 (1952), 468-519.
doi: 10.2307/1969644. |
[24] |
W. H. Fleming and M. Viot, Some measure-valued Markov processes in population genetics theory, Indiana Univ. Math. J., 28 (1979), 817-843.
doi: 10.1512/iumj.1979.28.28058. |
[25] |
H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1980. |
[26] |
G. Köthe, Topological Vector Spaces II, Springer Verlag, Berlin-Heidelberg-New York, 1979. |
[27] |
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
[28] |
G. Metafune, Analiticity for some degenerate one-dimensional evolution equations, Studia Math., 127 (1998), 251-276. |
[29] |
R. Nagel, One-Parameter Semigroups of Positive Operators, Lect. Notes Math., 1184, Springer, 1986. |
[30] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[31] |
S. Pal, Analysis of the market weights under the volatility-stabilized market mode, Ann. App. Prob., 21 (2011), 1180-2013.
doi: 10.1214/10-AAP725. |
[32] |
N. Shimakura, Equations différentielles provenant de la génétique des populations, Tôhoku Math. J., 77 (1977), 287-318. |
[33] |
N. Shimakura, Formulas for diffusion approximations of some gene frequency models, J. Math. Kyoto Univ., 21 (1981), 19-45. |
[34] |
N. Shimakura, Partial Differential Operators of Elliptic Type, Translations of Mathematical Monographs, 99, Amer. Math. Soc., Providence, 1992. |
[35] |
W. Stannat, On the validity of the logarithmic-Sobolev inequality for symmetric Fleming-Viot operators, Annals Prob., 28 (2000), 667-684.
doi: 10.1214/aop/1019160256. |
[36] |
F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, London, 1967. |
show all references
References:
[1] |
A. A. Albanese, M. Campiti and E. Mangino, Approximation formulas for $C_0$-semigroups and their resolvent, J. Appl. Funct. Anal., 1 (2006), 343-358. |
[2] |
A. A. Albanese, M. Campiti and E. Mangino, Regularity properties of semigroups generated by some Fleming-Viot type operators, J. Math. Anal. Appl., 335 (2007), 1259-1273.
doi: 10.1016/j.jmaa.2007.02.042. |
[3] |
A. A. Albanese and E. Mangino, A class of non-symmetric forms on the canonical simplex of $S^d$, Discrete and Continuous Dynamical Systems-Series A, 23 (2009), 639-654.
doi: 10.3934/dcds.2009.23.639. |
[4] |
A. A. Albanese and E. Mangino, Analyticity of a class of degenerate evolution equations on the simplex of $S^d$ arising from Fleming-Viot processes, J. Math. Anal. Appl., 379 (2011), 401-424.
doi: 10.1016/j.jmaa.2011.01.015. |
[5] |
A. A. Albanese and E. Mangino, One-dimensional degenerate diffusion operators, Mediterr. J. Math., 10 (2013), 707-729.
doi: 10.1007/s00009-013-0279-8. |
[6] |
S. Angenent, Local existence and regularity for a class of degenerate parabolic equations, Math. Ann., 280 (1988), 465-482.
doi: 10.1007/BF01456337. |
[7] |
S. R. Athreya, R. F. Bass and E. A. Perkins, Hölder norm estimates for elliptic operators on finite and infinite-dimensional spaces, Trans. Amer. Math. Soc., 357 (2005), 5001-5029.
doi: 10.1090/S0002-9947-05-03638-X. |
[8] |
R. F. Bass and E. A. Perkins, Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains, Trans. Amer. Math. Soc., 355 (2002), 373-405.
doi: 10.1090/S0002-9947-02-03120-3. |
[9] |
H. Brezis, W. Rosenkrants and B. Singer, On a degenerate elliptic-parabolic equation occurring in the theory of probability, Comm. Pure Appl. Math., 24 (1971), 395-416.
doi: 10.1002/cpa.3160240305. |
[10] |
M. Campiti and G. Metafune, Ventcel's boundary conditions and analytic semigroups, Arch. Math., 70 (1998), 377-390.
doi: 10.1007/s000130050210. |
[11] |
M. Campiti and I. Rasa, Qualitative properties of a class of Fleming-Viot operators, Acta Math. Hungar., 103 (2004), 55-69.
doi: 10.1023/B:AMHU.0000028236.59446.da. |
[12] |
S. Cerrai and P. Clément, On a class of degenerate elliptic operators arising from the Fleming-Viot processes, J. Evol. Equ., 1 (2001), 243-276.
doi: 10.1007/PL00001370. |
[13] |
S. Cerrai and P. Clément, Schauder estimates for a degenerate second-order elliptic operator on a cube, J. Differential Equations, 242 (2007), 287-321.
doi: 10.1016/j.jde.2007.08.002. |
[14] |
P. Clément and C. A. Timmermans, On $C_0$-semigroup generated by differential operators satisfying Ventcel's boundary conditions, Indag. Math., 89 (1986), 379-387. |
[15] |
J. R. Dorroh, Contraction semi-groups in a function space, Pacific J. Math., 19 (1966), 35-38.
doi: 10.2140/pjm.1966.19.35. |
[16] |
K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, 194, Springer, New York, Berlin, Heildelberg, 2000. |
[17] |
C. L. Epstein and R. Mazzeo, Wright-Fisher diffusion in one dimension, SIAM J. Math. Anal., 42 (2010), 1429-1436.
doi: 10.1137/090766152. |
[18] |
C. L. Epstein and R. Mazzeo, Degenerate Diffusion Operators Arising in Population Biology, Annals of Math. Studies, Princeton University Press, 2012. |
[19] |
S. N. Ethier, A class of degenerate diffusion processes occurring in population genetics, Comm. Pure Appl. Math., 29 (1976), 483-493.
doi: 10.1002/cpa.3160290503. |
[20] |
S. N. Ethier and T. G. Kurtz, Markov Processes, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, 1986.
doi: 10.1002/9780470316658. |
[21] |
S. N. Ethier and T. G. Kurtz, Fleming-Viot processes in population genetics, SIAM J. Control Optim., 31 (1993), 345-386.
doi: 10.1137/0331019. |
[22] |
W. Feller, Two singular diffusion problems, Ann. of Math., 54 (1951), 173-181.
doi: 10.2307/1969318. |
[23] |
W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math., 55 (1952), 468-519.
doi: 10.2307/1969644. |
[24] |
W. H. Fleming and M. Viot, Some measure-valued Markov processes in population genetics theory, Indiana Univ. Math. J., 28 (1979), 817-843.
doi: 10.1512/iumj.1979.28.28058. |
[25] |
H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1980. |
[26] |
G. Köthe, Topological Vector Spaces II, Springer Verlag, Berlin-Heidelberg-New York, 1979. |
[27] |
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
[28] |
G. Metafune, Analiticity for some degenerate one-dimensional evolution equations, Studia Math., 127 (1998), 251-276. |
[29] |
R. Nagel, One-Parameter Semigroups of Positive Operators, Lect. Notes Math., 1184, Springer, 1986. |
[30] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[31] |
S. Pal, Analysis of the market weights under the volatility-stabilized market mode, Ann. App. Prob., 21 (2011), 1180-2013.
doi: 10.1214/10-AAP725. |
[32] |
N. Shimakura, Equations différentielles provenant de la génétique des populations, Tôhoku Math. J., 77 (1977), 287-318. |
[33] |
N. Shimakura, Formulas for diffusion approximations of some gene frequency models, J. Math. Kyoto Univ., 21 (1981), 19-45. |
[34] |
N. Shimakura, Partial Differential Operators of Elliptic Type, Translations of Mathematical Monographs, 99, Amer. Math. Soc., Providence, 1992. |
[35] |
W. Stannat, On the validity of the logarithmic-Sobolev inequality for symmetric Fleming-Viot operators, Annals Prob., 28 (2000), 667-684.
doi: 10.1214/aop/1019160256. |
[36] |
F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, London, 1967. |
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