Boundary value problems for Dirac-type equations

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 579, 2005, Pages 13-73

  Bartnik, Robert A ^a,b   Chruściel, Piotr T ^a,c  

^a University of Canberra ^*

^b UNIVERSITY OF CANBERRA   (Australia)

^c UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21644469571     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/crll.2005.2005.579.13     Document Type: Article

References (31)

1. M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), 3-38.
2. M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Camb. Phil. Soc. 77 (1975), 43-69.
3. A. Axelsson, R. Grognard, J. Hogan, and A. McIntosh, Harmonic analysis of Dirac operators in Lipschitz domains, Clifford analysis and its applications (Prague 2000), V. Soucek, F. Brackx, J. S. R. Chisholm, eds., NATO Sci. Ser. II, Kluwer (2001), 231-246.
4. C. Bär, Lower eigenvalue estimates for Dirac operators, Math. Ann. 293 (1992), 39-46.
5. B. Booß and K. P. Wojciechowski, Elliptic boundary problems for Dirac operators, Birkhäuser, Boston 1993.
6. U. Bunke, Comparison of Dirac operators on manifolds with boundary, Rend. Circ. Mat. Palermo (2) Suppl. (1993), 133-141, Proceedings of the Winter School "Geometry and Physics" (Srní 1991).
7. Gilles Canon, Un théorème de l'indice relatif, Sém. Th. Spectr. Géom. 15, Univ. Grenoble I, Saint (1996-97), 193-202.
8. P. T. Chruściel, Quelques inégalités dans les espaces de Sobolev à poids, Tours preprint, unpublished, http:// www.phys.univ-tours.fr/~piotr/papers/wpi, 1987.
9. A. J. Dougan and L. J. Mason, Quasi-local mass constructions with positive gravitational energy, Phys. Rev. Lett. 67 (1991), 2119-2123.
10. R. Geroch and S.-M. Perng, Total mass-momentum of arbitrary initial data sets in general relativity, J. Math. Phys. 35 (1994), 4157-4177.
11. D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, 2 ed., Springer Verlag, 1977.
12. M. Herzlich, A Penrose-like inequality for the mass on Riemannian asymptotically flat manifolds, Commun. Math. Phys. 188 (1997), 121-133.
13. M. Herzlich, The positive mass theorem for black holes revisited, J. Geom. Phys. 26 (1998), 97-111.
14. O. Hijazi, Première valeur propre de l'opérateur de Dirac et nombre de Yamabe, C.R. Acad. Sci. Paris 313 (1991), 865-868.
15. L. Hörmander, The analysis of partial differential operators, III, Grundl. Math. Wiss. 224, Springer Verlag, 1985.
16. G. T. Horowitz, G. W. Gibbons, S. W. Hawking, and M. J. Perry, Positive mass theorems for black holes, Commun. Math. Phys. 88 (1983), 295-308.
17. H. B. Lawson and M. L. Michelsohn, Spin geometry, Princeton Math. Ser. 38, Princeton, UP, 1989.
18. A. Lichnerowicz, Spineurs harmonique, C.R. Acad. Sci. Paris Sér. A-B 257 (1963), 7-9.
19. J. Marschall, Pseudo-differential operators with coefficients in Sobolev spaces, Trans. AMS 307 (1988), 335-361.
20. A. McIntosh, D. Mitrea, and M. Mitrea, Rellich type estimates for one-sided mongenic functions in Lipschitz domains and applications, Analytical and Numerical Methods in Quaternionic and Clifford algebras, K. Gürlbeck and W. Sprössig, eds. (1996), 135-143.
21. H. P. McKean, An upper bound to the spectrum of A on a manifold of negative curvature, J. Diff. Geom. 4 (1970), 359-366.
22. C. B. Morrey, Multiple integrals in the calculus of variation, Springer Verlag, Berlin-Heidelberg-New York 1966.
23. C. B. Morrey, Jr., Multiple integrals in the calculus of variations, Springer Verlag, 1966.
24. T. Parker and C. Taubes, On Witten's proof of the positive energy theorem, Commun. Math. Phys. 84 (1982), 223-238.
25. E. Schrödinger, Diracsches Elektron im Schwerfeld, Preuss. Akad. Wiss. Phys.-Math. 11 (1932), 436-460.
26. R. I. Seeley, Singular integrals and boundary problems, Am. J. Math. 88 (1966), 781-809.
27. K. Shiohama, Total curvature and minimal area of complete open surfaces, Proc. Am. Math. Soc. 94 (1985), 310-316.
28. M. E. Taylor, Partial differential equations III, Appl. Math. Sci. 117, Springer Verlag, 1996.
29. J. Weidmann, Linear operators in Hilbert spaces, Grad. Texts Math. 68, Springer Verlag, New York-Heidelberg-Berlin 1980.
30. E. Witten, A simple proof of the positive energy theorem, Comm. Math. Phys. 80 (1981), 381-402.
31. J. Wolf, Essential self-adjointness for the Dirac operator and its square, Indiana Univ. Math. J. 22 (1972/73), 611-640.