no. 1
Linear parabolic equations in Banach spaces with variable domains but constant interpolation spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 13 (1986) no. 1, pp. 75-107. 
@article{ASNSP_1986_4_13_1_75_0,
     author = {Acquistapace, Paolo and Terreni, Brunello},
     title = {Linear parabolic equations in {Banach} spaces with variable domains but constant interpolation spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {75--107},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 13},
     number = {1},
     year = {1986},
     mrnumber = {863636},
     zbl = {0612.34057},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1986_4_13_1_75_0/}
}
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Acquistapace, Paolo; Terreni, Brunello. Linear parabolic equations in Banach spaces with variable domains but constant interpolation spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 13 (1986) no. 1, pp. 75-107. http://www.numdam.org/item/ASNSP_1986_4_13_1_75_0/

[1] P. Acquistapace - B. Terreni, Some existence and regularity results for abstract non-autonomous parabolic equations, J. Math. Anal. Appl., 99 (1984), pp. 9-64. | MR | Zbl

[2] P. Acquistapace - B. Terreni, On the abstract non-autonomous Cauchy problem in the case of constant domains, Ann. Mat. Pura Appl., (4) 140 (1985), pp. 1-55. | MR | Zbl

[3] P. Acquistapace - B. Terreni, Maximal space regularity for abstract nonautonomous parabolic equations, J. Funct. Anal., 60 (1985), pp. 168-210. | MR | Zbl

[4] P. Acquistapace - B. Terreni, Characterization of Hölder and Zygmund classes as interpolation spaces, preprint, Dipartimento di Matematica, Univ. Pisa, no. 61 (1984). | MR

[5] S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math., 15 (1962), pp. 119-147. | MR | Zbl

[6] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math., 12 (1959), pp. 623-727. | MR | Zbl

[7] H. Amann, Periodic solutions of semilinear parabolic equations, in Nonlinear Analysis, L. Cesàri, R. Kannan, H. F. Weinberger editors, Academic Press, New York - San Francisco - London, 1978. | MR | Zbl

[8] P.L. Butzer - H. Berens, Semigroups of Operators and Approximation, Springer-Verlag, Berlin - Heidelberg - New York, 1967. | MR | Zbl

[9] P. Cannarsa - B. Terreni - V. Vespri, Analytic semigroups generated by non-variational elliptic systems of second order under Dirichlet boundary conditions, J. Math. Anal. Appl., 112 (1985), pp. 56-103. | MR | Zbl

[10] G. Da Prato - P. Grisvard, Sommes d'opérateurs linéaires et équations différentielles opérationelles, J. Math. Pures Appl., 54 (1975), pp. 305-387. | MR | Zbl

[11] G. Da Prato - P. Grisvard, Equations d'évolution abstraites non linéaires de type parabolique, Ann. Mat. Pura Appl., (4), 120 (1979), pp. 329-396. | MR | Zbl

[12] G. Da Prato - E. Sinestrari, Hölder regularity for nonautonomous abstract parabolic equations, Israel J. Math., 42 (1982), pp. 1-19. | MR | Zbl

[13] P. Grisvard, Equations différentielles abstraites, Ann. Sci. Ecole Norm. Sup., (4), 2 (1969), pp. 311-395. | Numdam | MR | Zbl

[14] P. Grisvard, Equations opérationelles abstraites et problèmes aux limites dans des domains non réguliers, Actes Congrés Intern. Math. (Nice, 1970), 2, Gauthier-Villars, Paris (1971), pp. 731-736. | MR | Zbl

[15] T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semigroups, Proc. Japan Acad. Ser. A Math. Sci., 35 (1959), pp. 467-468. | MR | Zbl

[16] T. Kato, Abstract evolution equations of parabolic type in Banach and Hilbert spaces, Nagoya Math. J., 19 (1961), pp. 93-125. | MR | Zbl

[17] T. Kato - H. Tanabe, On the abstract evolution equations, Osaka Math. J., 14 (1962), pp. 107-133. | MR | Zbl

[18] J.L. Lions, Théorèmes de trace et d'interpolation, I, Ann. Sc. Norm. Sup., (3), 13 (1959), pp. 389-403. | Numdam | MR | Zbl

[19] J.L. Lions, Espaces d'interpolation et domaines de puissances fractionnaires d'opérateurs, J. Math. Soc. Japan, 14 (1962), pp. 233-241. | MR | Zbl

[20] J.L. Lions, Remarques sur les espaces d'interpolation et les problèmes aux limites, in « Les équations aux dérivées partielles », Colloque no. 117 du C.N.R.S. (Paris, 1962), Editions du C.N.R.S., Paris, 1963, pp. 75-86. | MR | Zbl

[21] J.L. Lions - J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Etudes Sci. Publ. Math., 19 (1964), pp. 5-68. | Numdam | MR | Zbl

[22] A. Lunardi, Interpolation spaces between domains of elliptic operators and spaces of continuous functions with applications to nonlinear parabolic equations, Math. Nachr., 121 (1985), pp. 295-318. | MR | Zbl

[23] E.T. Poulsen, Evolutionsgleichungen in Banach Räumen, Math. Z., 90 (1965), pp. 289-309. | MR | Zbl

[24] R. Seeley, Norms and domains of the complex powers Az B, Amer. J. Math., 93 (1971), pp. 299-309. | MR | Zbl

[25] R. Seeley, Interpolation in Lp with boundary conditions, Studia Math., 44 (1972), pp. 47-60. | MR | Zbl

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

[27] P.E. Sobolevsk, First order differential equations in Hilbert space with a variable positive definite self-adjoint operator whose fractional power has a constant domain of definition, Dokl. Akad. Nauk, 123 (1958), pp. 984-987 (in Russian). | MR | Zbl

[28] P.E. Sobolevsk, Parabolic equations in a Banach space with an unbounded variable operator, a fractional power of which has a constant domain of definition, Dokl. Akad. Nauk, 138 (1961), pp. 59-62 (in Russian); English translation: Soviet Math. Dokl., 2 (1961), pp. 545-548. | MR | Zbl

[29] P.E. Sobolevski, On equations of parabolic type in Banach space, Trudy Moscow Mat. Obsc., 10 (1961), pp. 297-350 (in Russian); English translation Amer. Mat. Soc. Transl., 49 (1965), pp. 1-62. | MR

[30] H.B. Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans. Amer. Math. Soc., 199 (1974), pp. 141-162. | MR | Zbl

[31] H.B. Stewart, Generation of analytic semigroups by strongly elliptic operators under general boundary conditions, Trans. Amer. Math. Soc., 259 (1980), pp. 299-310. | MR | Zbl

[32] P. Suryanarayana, The higher order differentiability of solutions of abstract evolution equations, Pacific J. Math., 22 (1967), pp. 543-561. | MR | Zbl

[33] H. Tanabe, On the equations of evolution in a Banach space, Osaka Math. J., 12 (1960), pp. 363-376. | MR | Zbl

[34] H. Tanabe, Note on singular perturbation for abstract differential equations, Osaka J. Math., 1 (1964), pp. 239-252. | MR | Zbl

[35] H. Tanabe, Equations of Evolution, Pitman, London - San Francisco - Melbourne, 1979. | MR | Zbl

[36] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam - New York - Oxford, 1978. | MR | Zbl

[37] A. Yagi, On the abstract linear evolution equations in Banach spaces, J. Math. Soc. Japan, 28 (1976), pp. 290-303. | MR | Zbl

[38] A. Yagi, On the abstract evolution equation of parabolic type, Osaka J. Math., 14 (1977), pp. 557-568. | MR | Zbl