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.
@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] W. Arendt, Resolvent positive operators, Proc. London Math. Soc. 54 (1987), 321-349. | MR | Zbl

[Are87b] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-353. | MR | Zbl

[ArBe98] W. Arendt - Ph. Bénilan, 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] W. Arendt - J. Prüss, Vector-valued Tauberian theorems and asymptotic behaviour of linear Volterra equations, SIAM J. Math. Anal. 23 (1992), 412-448. | MR | Zbl

[Are94] W. Arendt, 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] W. Arendt - C.J.K. Batty, Principal eigenvalue and perturbation, In: "Operator Theory", Advances and Applications Vol. 75, Birkhäuser, Basel, 1995, p. 39-55. | MR | Zbl

[ArBa99] W. Arendt - C.J.K. Batty, Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line, Bull. London Math. Soc. 31 (1999), 291-304. | MR | Zbl

[BCP88] Ph. Bénilan - M. Crandall - A. Pazy, "Bonnes solutions" d'un problème d'évolution semi-linéaire, C.R. Acad. Sci. Paris 306 (1988), 527-530. | MR | Zbl

[Bre83] H. Brezis, "Analyse Fonctionnelle", Masson, Paris, 1983. | MR | Zbl

[BT97] G. Borgioli - S. Totaro, 3D-Streaming operator with multiplying boundary conditions: semigroup generation properties, Semigroup Forum 55 (1997), 110-117. | MR | Zbl

[BV62] I Babuška - R. Vyborny, Reguläre and stabile Randpunkte für das Problem der Wärmeleitungsgleichung, Ann. Polon. Math. 12 (1962), 19-104. | MR | Zbl

[Chi98] R. Chill, Tauberian theorems for vector-valued Fourier and Laplace transforms, Studia Math. 128 (1998), 55-69. | MR | Zbl

[CY77] C.Y. Chan - E.C. Young, Regular regions for parabolic and elliptic equations, Portugaliae Math. 36 (1977), 7-12. | MR | Zbl

[Dav89] B. Davies, "Heat Kernels and Spectrum Theory", Cambridge University Press, Cambridge, 1989. | Zbl

[DL87] R. Dautray - J.-L. Lions, "Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques", Masson, Paris, 1987. | MR | Zbl

[DS87] G. Da Prato - E. Sinestrari, Differential operators with non-dense domain, Annali Scuola Norm. Sup. Pisa Cl. Sci 14 (1987), 285-344. | Numdam | MR | Zbl

[E98] L.C. Evans, "Partial Differential Equations", Amer. Math. Soc., Providence, Rhode Island, 1998. | MR

[Fin74] A.M. Fink, "Almost Periodic Differential Equations ", Lecture Notes in Math. Springer Vol. 377, Berlin, 1977. | Zbl

[Fri59] A. Friedman, Convergence of solutions of parabolic equations to a steady state, J. Math. Mech. 8 (1959), 57-76. | MR | Zbl

[Ful56] W. Fulks, A note on the steady state solutions of the heat equation, Proc. Amer. Math. Soc. 7 (1956), 766-771. | MR | Zbl

[Ful57] W. Fulks, Regular regions for the heat equation, Pacific J. Math. 7 (1957), 867-877. | MR | Zbl

[Gre87] G. Greiner, Perturbing the boundary conditions of a generator, Houston J. Math. 13 (1987), 213-229. | MR | Zbl

[GT77] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer, Berlin, 1977. | MR | Zbl

[Hel69] L.L. Helms, "Introduction to Potential Theory", Wiley Interscience, New York, 1969. | MR | Zbl

[HP57] E. Hille - R. Phillips, "Functional Analysis and Semi-groups ", Amer. Math. Soc. Colloq. Publ., Vol. 31, Amer. Math. Soc. Providence, Rhode Island, 1957. | MR | Zbl

[Jos98] J Jost, "Partielle Differentialgleichungen", Springer, Berlin, 1998. | Zbl

[Kel67] O.D. Kellogg, "Foundations of Pontential Theory", Springer, Berlin, 1967. | MR | Zbl

[KH89] H. Kellermann - M. Hieber, Integrated semigroups, J. Functional Anal. 94 (1989), 160-180. | MR | Zbl

[Lan72] N.S. Landkof, "Foundations of Modem Potential Theory ", Springer, Berlin, 1972. | MR | Zbl

[LSW63] W. Littman - G. Stampacchia - H.F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (1963), 43-47. | Numdam | MR | Zbl

[Lum75] G. Lumer, Problème de Cauchy avec valeurs au bord continues, Comptes Rendues Acad. Sci. Paris 281 (1975), 805-808. | MR | Zbl

[LP76] G. Lumer - L. Paquet, 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] G. Lumer - R. Schnaubelt, Local operator methods and time dependentparabolic equations on non-cylindrical domains, Preprint 1999. | MR

[Lun95] A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems", Birkhäuser Basel, 1995. | MR | Zbl

[Ner96] J.M.A.M. Van Neerven, "The Asymptotic Behaviour of Semigroups of Operators", Birkhäuser, Basel, 1996. | Zbl

[Nus84] R.D. Nussbaum, Positive operators and elliptic eigenvalue problems, Math. Z. 186 (1984), 247-264. | MR | Zbl

[NS94] R. Nagel - E. Sinestrari, 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] J Prüß, "Evolutionary Integral Equations and Applications", Birkhäuser, Basel, 1993. | MR | Zbl

[Paz83] A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations", Springer, Berlin, 1983. | MR | Zbl

[Sin85] E. Sinestrari, On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl. 107 (1985), 16-66. | MR | Zbl

[Sta65] G. Stampacchia, 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] H.R. Thieme, Remark on resolvent positive operators and their perturbation, Discrete and Continuous Dynamical Systems 4 (1998), 73-90. | MR | Zbl

[Thi97b] H.R. Thieme, 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] A. Tychonoff, Sur l'equation de la chaleur à plusieurs variables, Bull. Univ. Moscow, Ser. Int., Sect. A 1 (1938), 1-44. | JFM | Zbl

[Wid71]] D.V. Widder, "An Introduction to Transform Theory", Academic Press, New York, 1971. | Zbl