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Known and unknown results on elliptic boundary problems


Author: Gerd Grubb
Journal: Bull. Amer. Math. Soc. 43 (2006), 227-230
MSC (2000): Primary 35J25, 47B25; Secondary 35J67
DOI: https://doi.org/10.1090/S0273-0979-06-01114-1
Published electronically: March 8, 2006
MathSciNet review: 2216111
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  • [AS80] A. Alonso and B. Simon, The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators, J. Operator Theory 4 (1980), 251-279. MR 0595414 (81m:47038)
  • [AS81] A. Alonso and B. Simon, Addenda to ``The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators'', J. Operator Theory 6 (1981), 407. MR 0643699 (83a:47032)
  • [B56] M. S. Birman, On the theory of self-adjoint extensions of positive definite operators, Mat. Sb. 38: 80 (1956), 431-450 (Russian). MR 0080271 (18:220d)
  • [EM03] W. N. Everitt and L. Markus, Elliptic partial differential operators and symplectic algebra, Memoirs of Amer. Math. Soc. 162 (2003), Number 770. MR 1955204 (2004d:47054)
  • [EM05] W. N. Everitt and L. Markus, Complex symplectic spaces and boundary value problems, Bull. Amer. Math. Soc. 42 (2005), 461-500. MR 2163706
  • [EMP05] W. N. Everitt, L. Markus and M. Plum, An unusual self-adjoint linear partial differential operator, Trans. Amer. Math. Soc. 357 (2005), 1303-1324. MR 2115367 (2005j:35038)
  • [F34] K. Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann. 109 (1934), 465-487. MR 1512905
  • [G68] G. Grubb, A characterization of the non-local boundary value problems associated with an elliptic operator, Ann. Scuola Norm. Sup. Pisa 22 (1968), 425-513, from Stanford University dissertation, 1966. MR 0239269 (39:626)
  • [G70] G. Grubb, Les problèmes aux limites généraux d'un opérateur elliptique, provenant de la théorie variationnelle, Bull. Sci. Math. 94 (1970), 113-157, from Stanford University dissertation, 1966. MR 0280866 (43:6585)
  • [G71] G. Grubb, On coerciveness and semiboundedness of general boundary problems, Isr. J. Math. 10 (1971), 32-95. MR 0318665 (47:7212)
  • [G73] G. Grubb, Weakly semibounded boundary problems and sesquilinear forms, Ann. Inst. Fourier Grenoble 23 (1973), 145-194. MR 0344669 (49:9408)
  • [G73a] G. Grubb, Semibounded boundary problems for elliptic operators, AMS Proc. Symp. Pure Math. 23 (1973), 113-123. MR 0344668 (49:9407)
  • [G74] G. Grubb, Properties of normal boundary problems for elliptic even-order systems, Ann. Scuola Norm. Sup. Pisa 1 (ser. IV) (1974), 1-61. MR 0492833 (58:11895)
  • [G83] G. Grubb, Spectral asymptotics for the ``soft'' selfadjoint extension of a symmetric elliptic differential operator, J. Operator Theory 10 (1983), 9-20. MR 0715550 (84k:35107)
  • [H63] L. Hörmander, Linear Partial Differential Operators, Springer Verlag, Berlin, Heidelberg, 1963. MR 0161012 (28:4221)
  • [H66] L. Hörmander, Pseudo-differential operators and non-elliptic boundary problems, Ann. Math. 83 (1966), 129-209. MR 0233064 (38:1387)
  • [K47] M. G. Krein, Theory of self-adjoint extensions of symmetric semi-bounded operators and applications I, Mat. Sb. 20: 62 (1947), 431-495 (Russian). MR 0024574 (9:515c)
  • [LM68] J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Editions Dunod, Paris, 1968; English translation in Springer Grundlehren series, 1973. MR 0247243 (40:512)
  • [N29] J. von Neumann, Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren, Math. Ann. 102 (1929), 49-131.
  • [S66] R. T. Seeley, Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), 781-809. MR 0209915 (35:810)
  • [VG67] B. R. Vainberg and V. V. Grusin, Uniformly non-elliptic problems II, Mat. Sb. 73 (1967), 126-154; Math. USSR-Sb. 2 (1967), 111-133. MR 0217463 (36:552)
  • [V52] M. I. Vishik, On general boundary value problems for elliptic differential equations, Trudy Moskov. Mat. Obsv. 1 (1952), 187-246; Amer. Math. Soc. Transl. 24 (1963), 107-172.

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Additional Information

Gerd Grubb
Affiliation: Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
Email: grubb@math.ku.dk

DOI: https://doi.org/10.1090/S0273-0979-06-01114-1
Keywords: Elliptic boundary value problems, selfadjoint realizations, harmonic functions, Krein's soft extension
Received by editor(s): December 10, 2005
Received by editor(s) in revised form: January 19, 2006
Published electronically: March 8, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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