We study the analyticity of the semigroups generated by some degenerate second order differential operators in the space C([α,β]), where [α,β] is a bounded real interval. The asymptotic behaviour and regularity with respect to the space variable are also investigated.
@article{bwmeta1.element.bwnjournal-article-smv127i3p251bwm,
author = {G. Metafune},
title = {Analyticity for some degenerate one-dimensional evolution equations},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {251-276},
zbl = {0901.35048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv127i3p251bwm}
}
Metafune, G. Analyticity for some degenerate one-dimensional evolution equations. Studia Mathematica, Tome 129 (1998) pp. 251-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv127i3p251bwm/
[00000] [1] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, 1972.
[00001] [2] S. Angenent, Local existence and regularity for a class of degenerate parabolic equations, Math. Ann. 280 (1988), 465-482. | Zbl 0619.35114
[00002] [3] A. Attalienti and S. Romanelli, On some classes of analytic semigroups on C([a,b]) related to R- or Γ-admissible mappings, in: Evolution Equations, G. Ferreyra, G. Goldstein and F. Neubrander (eds.), Lecture Notes in Pure and Appl. Math. 168, Dekker, 1995, 29-34. | Zbl 0818.47036
[00003] [4] H. Brezis, W. Rosenkrantz and B. Singer, On a degenerate elliptic-parabolic equation occurring in the theory of probability, Comm. Pure Appl. Math. 24 (1971), 395-416. | Zbl 0206.11203
[00004] [5] M. Campiti and G. Metafune, Ventcel's boundary conditions and analytic semigroups, Arch. Math. (Basel), to appear. | Zbl 0909.34051
[00005] [6] M. Campiti, G. Metafune and D. Pallara, Degenerate self-adjoint evolution equations on the unit interval, Semigroup Forum, to appear.
[00006] [7] P. Clément and C. A. Timmermans, On -semigroups generated by differential operators satisfying Ventcel’s boundary conditions, Indag. Math. 89 (1986), 379-387. | Zbl 0618.47035
[00007] [8] A. Favini, J. Goldstein and S. Romanelli, Analytic semigroups on generated by some classes of second order differential operators, preprint, 1996. | Zbl 0939.47036
[00008] [9] A. Favini and S. Romanelli, Analytic semigroups on C([0,1]) generated by some classes of second order differential operators, Semigroup Forum, to appear. | Zbl 0910.47034
[00009] [10] W. Feller, Two singular diffusion problems, Ann. of Math. 54 (1951), 173-182. | Zbl 0045.04901
[00010] [11] W. Feller, The parabolic differential equations and the associated semi-groups of transformations, ibid. 55 (1952), 468-519. | Zbl 0047.09303
[00011] [12] G. Fichera, On a degenerate evolution problem, in: Partial Differential Equations with Real Analysis, H. Begeher and A. Jeffrey (eds.), Pitman Res. Notes Math. Ser. 263, Longman, 1992, 15-42. | Zbl 0806.35097
[00012] [13] R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Springer, 1986. | Zbl 0585.47030
[00013] [14] K. Taira, On the existence of Feller semigroups with boundary conditions, II, J. Funct. Anal. 129 (1995), 108-131. | Zbl 0898.47032
[00014] [15] C. A. Timmermans, On -semigroups in a space of bounded continuous functions in the case of entrance or natural boundary points, in: Approximation and Optimization, J. A. Gómez Fernández et al. (eds.), Lecture Notes in Math. 1354, Springer, 1988, 209-216.