Elliptic operators and the decomposition of tensor fields
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- by Murray Cantor PDF
- Bull. Amer. Math. Soc. 5 (1981), 235-262
References
- Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. MR 515141
- 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 125307, DOI 10.1002/cpa.3160120405
- Judith Meryl Arms, Arthur Eliot Fischer, and Jerrold Eldon Marsden, Une approche symplectique pour des théorèmes de décomposition en géométrie ou relativité générale, C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 13, Ai, A517–A520 (French, with English summary). MR 388447
- M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geometry 3 (1969), 379–392. MR 266084, DOI 10.4310/jdg/1214429060
- Jean-Pierre Bourguignon, David G. Ebin, and Jerrold E. Marsden, Sur le noyau des opérateurs pseudo-différentiels à symbole surjectif et non injectif, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 16, Aii, A867–A870. MR 402829
- Murray Cantor, The existence of non-trivial asymptotically flat initial data for vacuum spacetimes, Comm. Math. Phys. 57 (1977), no. 1, 83–96. MR 462440, DOI 10.1007/BF01651695
- Murray Cantor, A necessary and sufficient condition for York data to specify an asymptotically flat spacetime, J. Math. Phys. 20 (1979), no. 8, 1741–1744. MR 543911, DOI 10.1063/1.524259
- Murray Cantor, A necessary and sufficient condition for York data to specify an asymptotically flat spacetime, J. Math. Phys. 20 (1979), no. 8, 1741–1744. MR 543911, DOI 10.1063/1.524259
- M. Cantor, Perfect fluid flows over $\textbf {R}^{n}$ with asymptotic conditions, J. Functional Analysis 18 (1975), 73–84. MR 380872, DOI 10.1016/0022-1236(75)90030-0
- M. Cantor, Some problems of global analysis on asymptotically simple manifolds, Compositio Math. 38 (1979), no. 1, 3–35. MR 523260
- M. Cantor, Spaces of functions with asymptotic conditions on $R^{n}$, Indiana Univ. Math. J. 24 (1974/75), 897–902. MR 365621, DOI 10.1512/iumj.1975.24.24072
- Murray Cantor and Dieter Brill, The Laplacian on asymptotically flat manifolds and the specification of scalar curvature, Compositio Math. 43 (1981), no. 3, 317–330. MR 632432
- Y. Choquet-Bruhat and D. Christodoulou, Elliptic systems in $H_{s,\delta }$ spaces on manifolds which are Euclidean at infinity, Acta Math. 146 (1981), no. 1-2, 129–150. MR 594629, DOI 10.1007/BF02392460
- Demetrios Christodoulou, The boost problem for weakly coupled quasilinear hyperbolic systems of the second order, J. Math. Pures Appl. (9) 60 (1981), no. 1, 99–130. MR 616009
- David G. Ebin, The manifold of Riemannian metrics, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 11–40. MR 0267604 16. A. Fischer and J. Marsden, The initial value problem and the dynamical formulation of general relativity, General Relativity (S. Hawking and W. Israel, eds.), Cambridge Univ. Press, New York and London, 1979, pp. 138-211.
- Arthur E. Fischer and Jerrold E. Marsden, Linearization stability of nonlinear partial differential equations, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 2, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 219–263. MR 0383456
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR 0473443, DOI 10.1007/978-3-642-96379-7 18a. H. Helmholtz, Über Integrale der Hydrodynamischen Gleichungen, welch den Wirbelbewegungen, J. Reine Angew. Math. 55 (1858), 25-55.
- W. V. D. Hodge, The theory and applications of harmonic integrals, Cambridge, at the University Press, 1952. 2d ed. MR 0051571
- Kunihiko Kodaira, Harmonic fields in Riemannian manifolds (generalized potential theory), Ann. of Math. (2) 50 (1949), 587–665. MR 31148, DOI 10.2307/1969552
- J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443–492. MR 181815, DOI 10.1002/cpa.3160180305 19. S. Lang, Differentiable manifolds, Addison-Wesley, Reading, Mass., 1972.
- Robert B. Lockhart, Fredholm properties of a class of elliptic operators on noncompact manifolds, Duke Math. J. 48 (1981), no. 1, 289–312. MR 610188
- J. Marsden, Application of global analysis in mathematical physics, Carleton Mathematical Lecture Notes, No. 3, Carleton University, Department of Mathematics, Ottawa, Ont., 1973. MR 0646466
- Robert C. McOwen, The behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math. 32 (1979), no. 6, 783–795. MR 539158, DOI 10.1002/cpa.3160320604
- Robert C. McOwen, On elliptic operators in $\textbf {R}^{n}$, Comm. Partial Differential Equations 5 (1980), no. 9, 913–933. MR 584101, DOI 10.1080/03605308008820158
- 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. MR 0202511, DOI 10.1007/978-3-540-69952-1
- Charles B. Morrey Jr. and James Eells Jr., A variational method in the theory of harmonic integrals. I, Ann. of Math. (2) 63 (1956), 91–128. MR 87764, DOI 10.2307/1969992
- Louis Nirenberg and Homer F. Walker, The null spaces of elliptic partial differential operators in $\textbf {R}^{n}$, J. Math. Anal. Appl. 42 (1973), 271–301. Collection of articles dedicated to Salomon Bochner. MR 320821, DOI 10.1016/0022-247X(73)90138-8
- Richard S. Palais, Foundations of global non-linear analysis, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0248880
- Richard S. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965. With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. MR 0198494, DOI 10.1515/9781400882045
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
- Frank W. Warner, Foundations of differentiable manifolds and Lie groups, Scott, Foresman & Co., Glenview, Ill.-London, 1971. MR 0295244
- James W. York Jr., Covariant decompositions of symmetric tensors in the theory of gravitation, Ann. Inst. H. Poincaré Sect. A (N.S.) 21 (1974), 319–332. MR 373548 30. K. Yoshida, Functional analysis, 3rd ed., Springer-Verlag, New York, 1971.
Additional Information
- Journal: Bull. Amer. Math. Soc. 5 (1981), 235-262
- MSC (1980): Primary 58G99, 35J15
- DOI: https://doi.org/10.1090/S0273-0979-1981-14934-X
- MathSciNet review: 628659