@article{ASNSP_1984_4_11_4_593_0, author = {Amann, Herbert}, title = {Existence and regularity for semilinear parabolic evolution equations}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {593--676}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 11}, number = {4}, year = {1984}, mrnumber = {808425}, zbl = {0625.35045}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1984_4_11_4_593_0/} }
TY - JOUR AU - Amann, Herbert TI - Existence and regularity for semilinear parabolic evolution equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1984 SP - 593 EP - 676 VL - 11 IS - 4 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1984_4_11_4_593_0/ LA - en ID - ASNSP_1984_4_11_4_593_0 ER -
%0 Journal Article %A Amann, Herbert %T Existence and regularity for semilinear parabolic evolution equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1984 %P 593-676 %V 11 %N 4 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_1984_4_11_4_593_0/ %G en %F ASNSP_1984_4_11_4_593_0
Amann, Herbert. Existence and regularity for semilinear parabolic evolution equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 11 (1984) no. 4, pp. 593-676. http://www.numdam.org/item/ASNSP_1984_4_11_4_593_0/
[1] Sobolev Spaces, Academic Press, New York, 1975. | MR | Zbl
,[2] On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math., 15 (1962), pp. 119-147. | MR | Zbl
,[3] Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, II, Comm. Pure Appl. Math., 12 (1959), pp. 623-727 and 17 (1964), pp. 35-92. | MR | Zbl
- - ,[4] Periodic solutions of semilinear parabolic equations, in « Nonlinear Analysis: A Collection of Papers in Honour of Erich H. Rothe », edited by L. Cesari, R. Kannan, H. F. Weinberger, Academic Press, New York, 1978, pp. 1-29. | MR | Zbl
,[5] Gewöhnliche Differentialgleichungen, W. de Gruyter, Berlin, 1983. | MR
,[6] Parabolic evolution equations with nonlinear boundary conditions, Proc. AMS Summer Inst. Nonl. Funct. Anal., Berkeley, 1983, to appear. | MR | Zbl
,[7] On the abstract nonautonomous Cauchy problem in the case of constant domains, Ann. Mat. Pura Appl., to appear. | MR | Zbl
- ,[8] Some existence and regularity results for abstract nonautonomous parabolic equations, J. Math. Anal. Appl., 99 (1984), pp. 9-64. | MR | Zbl
- ,[9] Interpolation Spaces. An Introduction, Springer-Verlag, Berlin, 1976. | MR | Zbl
- ,[10] Local Semi-Dynamical Systems, Lecture Notes in Mathematics, no. 90, Springer-Verlag, Berlin, 1969. | MR | Zbl
- ,[11] On the spectral theory of elliptic operators, I, Math. Ann., 142 (1961), pp. 22-130. | MR | Zbl
,[12] Semi-Groups of Operators and Approximation, Springer-Verlag, Berlin, 1967. | MR | Zbl
- ,[13] Generation of analytic semigroups by elliptic operators of second order in Hölder spaces, Ann. Scuola Norm. Sup. Pisa, 8 (1981), pp. 495-512. | Numdam | MR | Zbl
,[14] Abstract differential equations, maximal regularity and linearization, preprint, Scuola Norm. Sup. Pisa, 1983. | MR
,[15] Sommes d'opérateurs linéaires et équations différentielles opérationelles, J. Math. Pures Appl., 54 (1975), pp. 305-387. | MR | Zbl
- ,[16] Equations d'évolution abstraites non lineaires de type parabolic, Ann. Mat. Pura Appl., (IV), 120 (1979), pp. 329-396. | MR | Zbl
- ,[17] Maximal regularity for evolution equations by interpolation and extrapolation, preprint, Scuola Norm. Sup. Pisa, 1982. | MR
- ,[18] Hölder regularity for nonautonomous abstract parabolic equations, Israel J. Math., 42 (1982), pp. 1-19. | MR | Zbl
- ,[19] One-Parameter Semigroups, Academic Press, London, 1980. | MR | Zbl
,[20] The Cauchy Problem, Addison-Wesley, Reading, Mass., 1983. | MR
,[21] Partial Differential Equations, Holt, Rinehard and Winston, New York, 1969. | MR | Zbl
,[22] Partial Differential Equations of Parabolic Type, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964. | MR | Zbl
,[23] Équations différentielles abstraites, Ann. Scient. Éc. Norm. Sup., Sér. 4, 2 (1969), pp. 311-395. | Numdam | MR | Zbl
,[24] Nonlinear Evolution Equations. Global Behaviour of Solutions, Lecture Notes in Math., no. 841, Springer-Verlag, Berlin, 1981. | MR | Zbl
,[25] Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., no. 840, Springer-Verlag, Berlin, 1981. | MR | Zbl
,[26] On the abstract evolution equation, Osaka Math. J., 14 (1962), pp. 107-133. | MR | Zbl
- ,[27] Halbgruppen und semilineare Anfangs-Randwertprobleme, Manuscripta Math., 12 (1974), pp. 121-152. | MR | Zbl
,[28] Existenz und Regularität von Lösungen semilinearer parabolischer Anfangs-Bandwertprobleme, Math. J., 142 (1975), pp. 131-160. | MR | Zbl
,[29] Integral Operators in Spaces of Summable Functions, Noordhoff, Leyden, 1976. | MR
- - - ,[30] Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1968. | MR
- - ,[31] Problemi ai limiti non omogenei (V), Ann. Scuola Norm. Sup. Pisa, 16 (1962), pp. 1-44. | Numdam | MR | Zbl
- ,[32] Nonhomogeneous Boundary Value Problems and Applications, I, II, Springer-Verlag, Berlin, 1972. | Zbl
- ,[33] Interpolation spaces between domains of elliptic operators and spaces of continuous functions with applications to nonlinear parabolic equations, Math. Nachr., to appear. | MR | Zbl
,[34] Abstract quasilinear parabolic equations, Math. Ann., 267 (1984), pp. 395-415. | MR | Zbl
,[35] Semilinear parabolic problems define semiflows on Ck spaces, Trans. Amer. Math. Soc., 278 (1983), pp. 21-55. | MR | Zbl
,[36] Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, 1966. | MR | Zbl
,[37] Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. | MR | Zbl
,[38] Interpolation in Lp with boundary conditions, Studia Math., 44 (1972), pp. 47-60. | MR | Zbl
,[39] On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl., to appear. | MR | Zbl
,[40] Semi-linear evolution equations in interpolation spaces, Nonlinear Analysis, Theory, Meth. & Appl., 1 (1977), pp. 249-261. | MR | Zbl
- ,[41] Equations of parabolic type in a Banach space, Amer. Math. Soc. Transl., Ser. 2, 49 (1966), pp. 1-62.
,[42] On boundary value problems for linear parabolic systems of differential equations of general form, Proc. Steklov Inst. Math., 83 (1965), pp. 1-184. | MR | Zbl
,[43] Equations of Evolution, Pitman, London, 1979. | MR | Zbl
,[44] On the equation of evolution in a Banach space, Osaka Math. J., 12 (1960), pp. 363-376. | MR | Zbl
,[45] Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam, 1978. | MR | Zbl
,[46] Theory of Function Spaces, Birkhäuser, Basel, 1983. | MR | Zbl
,[47] Gebrochene Potenzen eines elliptischen Operators und parabolische Differentiatgteichungen in Räumen hölderstetiger Funktionen, Nachr. Akad. Wiss. Göttingen, II. math.-phys. Kl., 11 (1972), pp. 231-258. | MR | Zbl
,[48] Einige Bemerkungen zu meiner Arbeit « Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen », Manuseripta math., 11 (1974), pp. 199-201. | MR | Zbl
,[49] Lineare und semilineare parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen, Abh. Math. Sem. Univ. Hamburg, 43 (1975), pp. 234-262. | MR | Zbl
,[50] Partielle Differentialgleichungen, Teubner, Stuttgart, 1981. | MR | Zbl
,[51] On the abstract linear evolution equations in Banach spaces, J. Math. Soc. Japan, 28 (1976), pp. 290-303. | MR | Zbl
,[52] Functional Analysis, Springer-Verlag, Berlin, 1965.
,[53] On the question of the solvability of initial-boundary value problems for quasilinear parabolic systems, Zap. Nauc. Sem. LOMI., 110 (1981), pp. 225-234 (1981) (in Russian). | MR | Zbl
- ,[54] A. G. HAčATRJAN, Estimates for sotutions of parabolic initial-boundary value problems in weighted Hölder norms, Proc. Steklov Inst. Math., 2 (1981), pp. 153-162. | MR | Zbl
-