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Generation of analytic semigroups by strongly elliptic operators under general boundary conditions. (English) Zbl 0451.35033

MSC:
35K35 Initial-boundary value problems for higher-order parabolic equations
47D03 Groups and semigroups of linear operators
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[1] Shmuel Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962), 119 – 147. · Zbl 0109.32701 · doi:10.1002/cpa.3160150203 · doi.org
[2] Shmuel Agmon, Lectures on elliptic boundary value problems, Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. · Zbl 0142.37401
[3] S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623 – 727. · Zbl 0093.10401 · doi:10.1002/cpa.3160120405 · doi.org
[4] Reiko Arima, On general boundary value problem for parabolic equations, J. Math. Kyoto Univ. 4 (1964), 207 – 243. · Zbl 0143.13902
[5] Felix E. Browder, On the spectral theory of elliptic differential operators. I, Math. Ann. 142 (1960/1961), 22 – 130. · Zbl 0104.07502 · doi:10.1007/BF01343363 · doi.org
[6] Параболические системы, Издат. ”Наука”, Мосцощ, 1964 (Руссиан). · Zbl 0121.31902
[7] R. S. Freeman and Martin Schechter, On the existence, uniqueness and regularity of solutions to general elliptic boundary-value problems, J. Differential Equations 15 (1974), 213 – 246. · Zbl 0279.35032 · doi:10.1016/0022-0396(74)90077-1 · doi.org
[8] Avner Friedman, Partial differential equations, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1969. · Zbl 0224.35002
[9] Yoshiki Higuchi, A priori estimates and existence theorem on elliptic boundary value problems for unbounded domains, Osaka J. Math. 5 (1968), 103 – 135. · Zbl 0169.13204
[10] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. · Zbl 0148.12601
[11] -, Semigroups and temporally inhomogeneous evolution equations, C.I.M.E. lecture notes, Varenna, 1963.
[12] Tosio Kato and Hiroki Tanabe, On the abstract evolution equation, Osaka Math. J. 14 (1962), 107 – 133. · Zbl 0106.09302
[13] Tosio Kato and Hiroki Tanabe, On the analyticity of solution of evolution equations, Osaka J. Math. 4 (1967), 1 – 4. · Zbl 0154.16403
[14] R. L. Lau, Elliptic equations with parameter and applications to parabolic problems, Ph.D. thesis, Yale University, 1967.
[15] K. Masuda, Manuscript for seminar at Kyoto Univ., 1970.
[16] -, Unpublished manuscript, 1972.
[17] Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. · Zbl 0142.38701
[18] O. A. Oleĭnik, Boundary-value problems for linear equations of elliptic parabolic type with discontinuous coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 3 – 20 (Russian).
[19] Z. G. Šeftel\(^{\prime}\), Estimates in \?_\? of solutions of elliptic equations with discontinuous coefficients and satisfying general boundary conditions and conjugacy conditions, Soviet Math. Dokl. 4 (1963), 321 – 324. · Zbl 0163.34901
[20] H. Bruce Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans. Amer. Math. Soc. 199 (1974), 141 – 162. · Zbl 0264.35043
[21] H. Bruce Stewart, Spectral theory of heterogeneous diffusion systems, J. Math. Anal. Appl. 54 (1976), no. 1, 59 – 78. · Zbl 0324.35072 · doi:10.1016/0022-247X(76)90235-3 · doi.org
[22] Hiroki Tanabe, On Green’s functions of elliptic and parabolic boundary value problems, Proc. Japan Acad. 48 (1972), 709 – 711. · Zbl 0277.35042
[23] W. v. Wahl, Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1972), 231 – 258 (German). · Zbl 0251.35052
[24] Wolf von Wahl, Einige Bemerkungen zu meiner Arbeit ”Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen” (Nachr. Akad. Wiss. Gottingen Math.-Phys. Kl. II 1972, 231 – 258), Manuscripta Math. 11 (1974), 199 – 201 (German, with English summary). · Zbl 0285.35039 · doi:10.1007/BF01184957 · doi.org
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