Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Generation of analytic semigroups by strongly elliptic operators


Author: H. Bruce Stewart
Journal: Trans. Amer. Math. Soc. 199 (1974), 141-162
MSC: Primary 35J30; Secondary 47D05
DOI: https://doi.org/10.1090/S0002-9947-1974-0358067-4
MathSciNet review: 0358067
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Strongly elliptic operators realized under Dirichlet boundary conditions in unbounded domains are shown to generate analytic semigroups in the topology of uniform convergence. This fact is applied to initial-boundary value problems for temporally homogeneous and temporally inhomogeneous parabolic equations.


References [Enhancements On Off] (What's this?)

  • [1] S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962), 119-147. MR 26 #5288. MR 0147774 (26:5288)
  • [2] -, Lectures on elliptic boundary value problems, Van Nostrand Math. Studies, no. 2, Van Nostrand, Princeton, N. J., 1965. MR 31 #2504. MR 0178246 (31:2504)
  • [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. MR 23 #A2610. MR 0125307 (23:A2610)
  • [4] R. Arima, On general boundary value problems for parabolic equations, J. Math. Kyoto Univ. 4 (1964), 207-243. MR 33 #6156. MR 0197997 (33:6156)
  • [5] F. E. Browder, On the spectral theory of elliptic differential operators. I, Math. Ann. 142 (1960/61), 22-130. MR 35 #804. MR 0209909 (35:804)
  • [6] S. D. Èidel'man, Parabolic systems, ``Nauka", Moscow, 1964; English transl., Noordhoff, Groningen; North-Holland, Amsterdam, 1969. MR 29 #4998; 40 #6023. MR 0252806 (40:6023)
  • [7] A. Friedman, Partial differential equations, Holt, Rinehart and Winston, New York, 1969. MR 0445088 (56:3433)
  • [8] E. Hille and R. S. Phillips, Functional analysis and semi-groups, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, R. I., 1957. MR 19, 664. MR 0089373 (19:664d)
  • [9] T. Kato, Perturbation theory for linear operators, Die Grundlehren der math. Wissenschaften, Band 132, Springer-Verlag, New York, 1966. MR 34 #3324. MR 0203473 (34:3324)
  • [10] -, Semigroups and temporally inhomogeneous evolution equations, C.I.M.E. lecture notes, Varenna, 1963.
  • [11] T. Kato and H. Tanabe, On the abstract evolution equation, Osaka Math. J. 14 (1962), 107-133. MR 25 #4367. MR 0140954 (25:4367)
  • [12] -, On the analyticity of solution of evolution equations, Osaka J. Math. 4 (1967), 1-4. MR 36 #5482. MR 0222430 (36:5482)
  • [13] J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, no. 17, Dunod, Paris, 1968. MR 40 #512. MR 0247243 (40:512)
  • [14a] K. Masuda, Manuscript for seminar at Kyoto Univ., 1970.
  • [14b] -, Manuscript, 1972.
  • [15] C. B. Morrey, Jr., Multiple integrals in the calculus of variations, Die Grundlehren der math. Wissenschaften, Band 130, Springer-Verlag, New York, 1966. MR 34 #2380. MR 0202511 (34:2380)
  • [16] H. Tanabe, On Green's functions of elliptic and parabolic boundary value problems, Proc. Japan Acad. 48 (1972), 709-711. MR 0346318 (49:11043)
  • [17] K. Yosida, Functional analysis, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 123, Academic Press, New York; Springer-Verlag, Berlin, 1968. MR 39 #741. MR 0239384 (39:741)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35J30, 47D05

Retrieve articles in all journals with MSC: 35J30, 47D05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0358067-4
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society