On abstract parabolic fundamental solutions

Herbert AMANN

doi:10.2969/jmsj/03910093

Herbert AMANN

著者情報

ジャーナルフリー

1987 年 39 巻 1 号 p. 93-116

DOI https://doi.org/10.2969/jmsj/03910093

詳細

Published: 1987 Received: 1984/12/24 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) P. Acquistapace and B. Terreni, Linear parabolic equations in Banach spaces with variable domain but constant interpolation spaces, Annali Scuola Norm. Sup. Pisa Ser. 4, 13 (1986), 75-107.
2) H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math., 45 (1983), 225-254.
3) H. Amann, Existence and regularity for semilinear parabolic evolution equations, Annali Scuola Norm. Sup. Pisa Ser. 4, 11(1984), 593-676.
4) H. Amann, Global existence for semilinear parabolic systems, J. Reine Angew. Math., 360 (1985), 47-83.
5) H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc., 293 (1986), 191-227.
6) J. Bergh and J. Loefstroem, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.
7) G. Da Prato and P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation, J. Functional Analysis, 58 (1984), 107-124.
8) E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
9) E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence, R. I., 1957.
10) T. Kato, Abstract evolution equations of parabolic type in Banach and Hilbert spaces, Nagoya Math. J., 19 (1961), 93-125.
11) T. Kato and H. Tanabe, On the abstract evolution equation, Osaka Math. J., 14 (1962), 107-133.
12) H. Komatsu, Fractional powers of operators, Pacific J. Math., 19 (1966), 285-346.
13) H. Komatsu, Fractional powers of operators, VI: Interpolation of non-negative operators and imbedding theorems, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 19 (1972), 1-63.
14) S. G. Krein, Linear Differential Equations in Banach Spaces, Amer. Math. Soc., Providence, R. I., 1972.
15) J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I, Springer, Berlin, 1972.
16) A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
17) R. Seeley, Norms and domains of the complex powers A^Z_B Amer. J. Math., 93 (1971), 299-309.
18) R. Seeley, Interpolation in L^P with boundary conditions, Studia Math., 44 (1972), 47-60.
19) P. E. Sobolevskii, Equations of parabolic type in a Banach space, Amer. Math. Soc. Transl. Ser. 2, 49 (1966), 1-62.
20) P. E. Sobolevskii, Parabolic equations in a Banach space with an unbounded variable operator, a fractional power of which has a constant domain of definition, Soviet Math. Dokl., 2 (1961), 545-548.
21) H. Tanabe, On the equation of evolution in a Banach space, Osaka Math. J., 12 (1960), 363-376.
22) H. Tanabe, Equations of Evolution, Pitman, London, 1979.
23) H. Tanabe, Note on Volterra integrodifferential equations of parabolic type, Preprint.
24) H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
25) A. Yagi, On the abstract linear evolution equations in Banach spaces, J. Math. Soc. Japan, 28 (1976), 290-303.
26) A. Yagi, On the abstract evolution equation of parabolic type, Osaka J. Math., 14 (1977), 557-568.
27) K. Yosida, Functional Analysis, Springer, Berlin, 1965.

Right : [1] P. Acquistapace and B. Terreni, Linear parabolic equations in Banach spaces with variable domain but constant interpolation spaces, Annali Scuola Norm. Sup. Pisa Ser. 4, 13 (1986), 75-107.
[2] H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math., 45 (1983), 225-254.
[3] H. Amann, Existence and regularity for semilinear parabolic evolution equations, Annali Scuola Norm. Sup. Pisa Ser. 4, 11(1984), 593-676.
[4] H. Amann, Global existence for semilinear parabolic systems, J. Reine Angew. Math., 360 (1985), 47-83.
[5] H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc., 293 (1986), 191-227.
[6] J. Bergh and J. Loefstroem, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.
[7] G. Da Prato and P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation, J. Functional Analysis, 58 (1984), 107-124.
[8] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
[9] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence, R. I., 1957.
[10] T. Kato, Abstract evolution equations of parabolic type in Banach and Hilbert spaces, Nagoya Math. J., 19 (1961), 93-125.
[11] T. Kato and H. Tanabe, On the abstract evolution equation, Osaka Math. J., 14 (1962), 107-133.
[12] H. Komatsu, Fractional powers of operators, Pacific J. Math., 19 (1966), 285-346.
[13] H. Komatsu, Fractional powers of operators, VI: Interpolation of non-negative operators and imbedding theorems, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 19 (1972), 1-63.
[14] S. G. Krein, Linear Differential Equations in Banach Spaces, Amer. Math. Soc., Providence, R. I., 1972.
[15] J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I, Springer, Berlin, 1972.
[16] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
[17] R. Seeley, Norms and domains of the complex powers A^Z_B Amer. J. Math., 93 (1971), 299-309.
[18] R. Seeley, Interpolation in L^P with boundary conditions, Studia Math., 44 (1972), 47-60.
[19] P. E. Sobolevskii, Equations of parabolic type in a Banach space, Amer. Math. Soc. Transl. Ser. 2, 49 (1966), 1-62.
[20] P. E. Sobolevskii, Parabolic equations in a Banach space with an unbounded variable operator, a fractional power of which has a constant domain of definition, Soviet Math. Dokl., 2 (1961), 545-548.
[21] H. Tanabe, On the equation of evolution in a Banach space, Osaka Math. J., 12 (1960), 363-376.
[22] H. Tanabe, Equations of Evolution, Pitman, London, 1979.
[23] H. Tanabe, Note on Volterra integrodifferential equations of parabolic type, Preprint.
[24] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
[25] A. Yagi, On the abstract linear evolution equations in Banach spaces, J. Math. Soc. Japan, 28 (1976), 290-303.
[26] A. Yagi, On the abstract evolution equation of parabolic type, Osaka J. Math., 14 (1977), 557-568.
[27] K. Yosida, Functional Analysis, Springer, Berlin, 1965.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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