@article{ASNSP_2000_4_29_3_639_0, author = {Arendt, Wolfgang}, title = {Resolvent positive operators and inhomogeneous boundary conditions}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {639--670}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 29}, number = {3}, year = {2000}, mrnumber = {1817713}, zbl = {1072.35077}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2000_4_29_3_639_0/} }
TY - JOUR AU - Arendt, Wolfgang TI - Resolvent positive operators and inhomogeneous boundary conditions JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2000 SP - 639 EP - 670 VL - 29 IS - 3 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2000_4_29_3_639_0/ LA - en ID - ASNSP_2000_4_29_3_639_0 ER -
%0 Journal Article %A Arendt, Wolfgang %T Resolvent positive operators and inhomogeneous boundary conditions %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2000 %P 639-670 %V 29 %N 3 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_2000_4_29_3_639_0/ %G en %F ASNSP_2000_4_29_3_639_0
Arendt, Wolfgang. Resolvent positive operators and inhomogeneous boundary conditions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 3, pp. 639-670. http://www.numdam.org/item/ASNSP_2000_4_29_3_639_0/
[Are87a] Resolvent positive operators, Proc. London Math. Soc. 54 (1987), 321-349. | MR | Zbl
,[Are87b] Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-353. | MR | Zbl
,[ArBe98] Wiener regularity and heat semigroups on spaces of continuous functions, In: "Progress in Nonlinear Differential Equations and Applications", Escher - Simonett, (eds.), Birkhäuser, Basel, 1998, pp. 29-49. | MR | Zbl
- ,[AP92] Vector-valued Tauberian theorems and asymptotic behaviour of linear Volterra equations, SIAM J. Math. Anal. 23 (1992), 412-448. | MR | Zbl
- ,[Are94] Vector-valued versions of some representation theorems in real analysis, In: "Functional Analysis", Proc. Essen 1991, K. Bierstedt, A. Pietsch, W. Ruess, D. Vogt (eds.), Marcel-Dekker 1994, 33-50. | MR | Zbl
,[ArBa95] Principal eigenvalue and perturbation, In: "Operator Theory", Advances and Applications Vol. 75, Birkhäuser, Basel, 1995, p. 39-55. | MR | Zbl
- ,[ArBa99] Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line, Bull. London Math. Soc. 31 (1999), 291-304. | MR | Zbl
- ,[BCP88] "Bonnes solutions" d'un problème d'évolution semi-linéaire, C.R. Acad. Sci. Paris 306 (1988), 527-530. | MR | Zbl
- - ,[Bre83] Analyse Fonctionnelle", Masson, Paris, 1983. | MR | Zbl
, "[BT97] 3D-Streaming operator with multiplying boundary conditions: semigroup generation properties, Semigroup Forum 55 (1997), 110-117. | MR | Zbl
- ,[BV62] Reguläre and stabile Randpunkte für das Problem der Wärmeleitungsgleichung, Ann. Polon. Math. 12 (1962), 19-104. | MR | Zbl
- ,[Chi98] Tauberian theorems for vector-valued Fourier and Laplace transforms, Studia Math. 128 (1998), 55-69. | MR | Zbl
,[CY77] Regular regions for parabolic and elliptic equations, Portugaliae Math. 36 (1977), 7-12. | MR | Zbl
- ,[Dav89] Heat Kernels and Spectrum Theory", Cambridge University Press, Cambridge, 1989. | Zbl
, "[DL87] Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques", Masson, Paris, 1987. | MR | Zbl
- , "[DS87] Differential operators with non-dense domain, Annali Scuola Norm. Sup. Pisa Cl. Sci 14 (1987), 285-344. | Numdam | MR | Zbl
- ,[E98] Partial Differential Equations", Amer. Math. Soc., Providence, Rhode Island, 1998. | MR
, "[Fin74] Almost Periodic Differential Equations ", Lecture Notes in Math. Springer Vol. 377, Berlin, 1977. | Zbl
, "[Fri59] Convergence of solutions of parabolic equations to a steady state, J. Math. Mech. 8 (1959), 57-76. | MR | Zbl
,[Ful56] A note on the steady state solutions of the heat equation, Proc. Amer. Math. Soc. 7 (1956), 766-771. | MR | Zbl
,[Ful57] Regular regions for the heat equation, Pacific J. Math. 7 (1957), 867-877. | MR | Zbl
,[Gre87] Perturbing the boundary conditions of a generator, Houston J. Math. 13 (1987), 213-229. | MR | Zbl
,[GT77] Elliptic Partial Differential Equations of Second Order", Springer, Berlin, 1977. | MR | Zbl
- , "[Hel69] Introduction to Potential Theory", Wiley Interscience, New York, 1969. | MR | Zbl
, "[HP57] Functional Analysis and Semi-groups ", Amer. Math. Soc. Colloq. Publ., Vol. 31, Amer. Math. Soc. Providence, Rhode Island, 1957. | MR | Zbl
- , "[Jos98] Partielle Differentialgleichungen", Springer, Berlin, 1998. | Zbl
, "[Kel67] Foundations of Pontential Theory", Springer, Berlin, 1967. | MR | Zbl
, "[KH89] Integrated semigroups, J. Functional Anal. 94 (1989), 160-180. | MR | Zbl
- ,[Lan72] Foundations of Modem Potential Theory ", Springer, Berlin, 1972. | MR | Zbl
, "[LSW63] Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (1963), 43-47. | Numdam | MR | Zbl
- - ,[Lum75] Problème de Cauchy avec valeurs au bord continues, Comptes Rendues Acad. Sci. Paris 281 (1975), 805-808. | MR | Zbl
,[LP76] Semi-groupes holomorphes, produit tensoriel de Semi-groupes et équations d'évolution, Séminaire: Théorie du Potentiel, Lecture Notes in Math. Vol. 563, Springer (1976), pp. 202-218. | MR | Zbl
- ,[LS99] Local operator methods and time dependentparabolic equations on non-cylindrical domains, Preprint 1999. | MR
- ,[Lun95] Analytic Semigroups and Optimal Regularity in Parabolic Problems", Birkhäuser Basel, 1995. | MR | Zbl
, "[Ner96] The Asymptotic Behaviour of Semigroups of Operators", Birkhäuser, Basel, 1996. | Zbl
, "[Nus84] Positive operators and elliptic eigenvalue problems, Math. Z. 186 (1984), 247-264. | MR | Zbl
,[NS94] Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, In: "Functional Analysis" , K. D. Bierstedt - A. Pietsch - W. M. Ruess, D. Vogt (eds). Lecture Notes Pure Appl. Math., Vol. 150 (1994), pp. 51-70. | MR | Zbl
- ,[P93] Evolutionary Integral Equations and Applications", Birkhäuser, Basel, 1993. | MR | Zbl
, "[Paz83] Semigroups of Linear Operators and Applications to Partial Differential Equations", Springer, Berlin, 1983. | MR | Zbl
, "[Sin85] On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl. 107 (1985), 16-66. | MR | Zbl
,[Sta65] Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier Grenoble 15 (1965), 189-258. | Numdam | MR | Zbl
,[Thi97a] Remark on resolvent positive operators and their perturbation, Discrete and Continuous Dynamical Systems 4 (1998), 73-90. | MR | Zbl
,[Thi97b] Positive perturbation of operator semigroups: Growth bounds essential compactness, and asymchronous exponential growth, Discrete and Continuous Dynamical Systems 4 (1998), 735-764. | MR | Zbl
,[Tyc38] Sur l'equation de la chaleur à plusieurs variables, Bull. Univ. Moscow, Ser. Int., Sect. A 1 (1938), 1-44. | JFM | Zbl
,[Wid71]] An Introduction to Transform Theory", Academic Press, New York, 1971. | Zbl
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