Known and unknown results on elliptic boundary problems

Bulletin of the American Mathematical Society

Volumn 43, Issue 2, 2006, Pages 227-230

  Grubb, Gerd ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Elliptic boundary value problems; Harmonic functions; Krein's soft extension; Selfadjoint realizations

Indexed keywords

EID: 33646431703     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-06-01114-1     Document Type: Review

References (25)

1. [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. MR0595414 (81m:47038)
2. [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. MR0643699 (83a:47032)
3. [B56] M. S. Birman, On the theory of self-adjoint, extensions of positive definite operators, Mat. Sb. 38: 80 (1956), 431-450 (Russian). MR0080271 (18:220d)
4. [EM03] W. N. Everitt and L. Markus, Elliptic partial differential operators and symplectic algebra, Memoirs of Amer. Math. Soc. 162 (2003), Number 770. MR1955204 (2004d:47054)
5. [EM05] W. N. Everitt and L. Markus, Complex symplectic spaces and boundary value problems, Bull. Amer. Math. Soc. 42 (2005), 461-500. MR2163706
6. [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. MR2115367 (2005j:35038)
7. [F34] K. Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann. 109 (1934), 465-487. MR1512905
8. [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. MR0239269 (39:626)
9. [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. MR0280866 (43:6585)
10. [G71] G. Grubb, On coerciveness and semiboundedness of general boundary problems, Isr. J. Math. 10 (1971), 32-95. MR0318665 (47:7212)
11. [G73] G. Grubb, Weakly semibounded boundary problems and sesquilinear forms, Ann. Inst. Fourier Grenoble 23 (1973), 145-194. MR0344669 (49:9408)
12. [G73a] G. Grubb, Semibounded boundary problems for elliptic operators, AMS Proc. Symp. Pure Math. 23 (1973), 113-123. MR0344668 (49:9407)
13. [G74] G. Grubb, Properties of normal boundary problems for elliptic even-order systems, Ann. Scuola Norm. Sup. Pisa 1 (ser. IV) (1974), 1-61. MR0492833 (58:11895)
14. [G83] G. Grubb, Spectral asymptotics for the "soft" selfadjoint extension of a symmetric elliptic differential operator, J. Operator Theory 10 (1983), 9-20. MR0715550 (84k:35107)
15. [H63] L. Hörmander, Linear Partial Differential Operators, Springer Verlag, Berlin, Heidelberg, 1963. MR0161012 (28:4221)
16. [H66] L. Hörmander, Pseudo-differential operators and non-elliptic boundary problems, Ann. Math. 83 (1966), 129-209. MR0233064 (38:1387)
17. [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). MR0024574 (9:515c)
18. [LM68] J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Editions Dunod, Paris, 1968;
19. English translation in Springer Grundlehren series, 1973. MR0247243 (40:512)
20. [N29] J. von Neumann, Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren, Math. Ann. 102 (1929), 49-131.
21. [S66] R. T. Seeley, Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), 781-809. MR0209915 (35:810)
22. [VG67] B. R. Vainberg and V. V. Grusin, Uniformly non-elliptic problems II, Mat. Sb. 73 (1967). 126-154;
23. Math. USSR-Sb. 2 (1967), 111-133. MR0217463 (36:552)
24. [V52] M. I. Vishik, On general boundary value problems for elliptic differential equations, Trudy Moskov. Mat. Obsv. 1 (1952). 187-246;
25. Amer. Math. Soc. Transl. 24 (1963), 107-172.