Elliptic differential operators on noncompact manifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 12 (1985) no. 3, p. 409-447
@article{ASNSP_1985_4_12_3_409_0,
     author = {Lockhart, Robert B. and Mc Owen, Robert C.},
     title = {Elliptic differential operators on noncompact manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 12},
     number = {3},
     year = {1985},
     pages = {409-447},
     zbl = {0615.58048},
     mrnumber = {837256},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1985_4_12_3_409_0}
}
Lockhart, Robert B.; Mc Owen, Robert C. Elliptic differential operators on noncompact manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 12 (1985) no. 3, pp. 409-447. https://www.numdam.org/item/ASNSP_1985_4_12_3_409_0/

[1] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations with general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), pp. 35-92. | MR 162050 | Zbl 0123.28706

[2] S. Agmon - L. Nirenberg, Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math., 16 (1963), pp. 121-239. | MR 155203 | Zbl 0117.10001

[3] M.S. Agranovi - M.I. Vi, Elliptic boundary value problems depending on a parameter, Dokl. Akad. Nauk SSSR, 149 (1963), pp. 223-226 = Soviet Math. Dokl., 4 (1963), pp. 325-329. | MR 146529 | Zbl 0145.14701

[4] R. Beals, A general calculus of pseudo differential operators, Duke Math. J., 42 (1975), pp. 1-42. | MR 367730 | Zbl 0343.35078

[5] M. Cantor, Some problems of global analysis on asymptotically simple manifolds, Compositio Math., 38 (1979), pp. 3-35. | Numdam | MR 523260 | Zbl 0402.58004

[6] J. Cheeger, On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci., 76 (1979), pp. 2103-2106. | MR 530173 | Zbl 0411.58003

[7] J. Cheeger - M. Goresky - R. Macpherson, L2-cohomology and intersection homology of singular algebraic varieties, Seminar on Differential Geometry (S. T. Yau ed.), Princeton Univ. Press, 1982, Princeton, N. J. | MR 645745 | Zbl 0503.14008

[8] Y. Choquet-Bruhat - D. Christodoulou, Elliptic systems in Hs,δ spaces on manifolds which are Euclidean at infinity, Acta Math., 146 (1981), pp. 129-150. | Zbl 0484.58028

[9] H.O. Cordes - E. Herman, Gel'fand theory of pseudo-dif f erential operators, Amer. J. Math., 90 (1968), pp. 681-717. | MR 454743 | Zbl 0169.47105

[10] A. Douglis - L. Nirenberg, Interior estimates for elliptic systems of partial differential equations, Comm. Pure Appl. Math., 8 (1955), pp. 503-538. | MR 75417 | Zbl 0066.08002

[11] L. Hörmander, Pseudo-differential operators and nonelliptic boundary problems, Ann. of Math., 83 (1966), pp. 129-209. | MR 233064 | Zbl 0132.07402

[12] R. Illner, Algebras of pseudo-differential operators in Lp(Rn), Comm. Partial Diff. Eq., 2 (1977), pp. 359-393. | MR 442758 | Zbl 0352.47021

[13] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, 1966, New York. | MR 203473 | Zbl 0148.12601

[14] V.A. Kondrat'Ev, Boundary value problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc., 16 (1967). | MR 226187 | Zbl 0194.13405

[15] H. Kumano-Go, Oscillatory integrals of symbols of pseudo-dif f erential operators on Rn, and operators of Fredholm type, Proc. Japan Acad., 49 (1973), pp. 397-402. | MR 355693 | Zbl 0272.47032

[16] R. Lockhart, Fredholm properties of a class of elliptic operators on noncompact manifolds, Duke Math. J., 48 (1981), pp. 289-312. | MR 610188 | Zbl 0486.35027

[17] R. Lockhart - R. Mcowen, On elliptic systems in Rn, Acta Math., 150 (1983), pp. 125-135. | MR 697610 | Zbl 0517.35031

[17a] R. Lockhart - R. Mcowen, Correction for on elliptic systems in Rn, Acta Math. 153 (1984), pp. 303-304. | MR 766267 | Zbl 0569.35027

[18] V.G. Maz'Ja - B.A. Plamenevski, Estimates in Lp and Hölder classes and the Miranda-Agmon .Maximum principle for solutions of elliptic boundary problems in domains with singular points on the boundary (in Russian), Math. Nachr., 81 (1978), pp. 25-82. | MR 492821 | Zbl 0371.35018

[19] R. Mcowen, Behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math., 32 (1979), pp. 783-795. | MR 539158 | Zbl 0426.35029

[20] R. Mcowen, Boundary value problems for the Laplacian in an exterior domain, Comm. Partial Diff. Eq., 6 (1981), pp. 783-798. | MR 623645 | Zbl 0473.35036

[21] R. Mcowen, Fredholm theory of partial differential equations on complete Riemannian manifolds, Pacific J. Math., 87 (1980), pp. 169-185. | MR 590874 | Zbl 0457.35084

[22] R. Mcowen, On elliptic operators in Rn, Comm. Partial Diff. Eq., 5 (1980), pp. 913-933. | MR 584101 | Zbl 0448.35042

[23] R. Melrose - G. Mendoza, Elliptic operators of totally characteristic type, preprint.

[24] L. Nirenberg - H.F. Walker, The nullspaces of elliptic partial differential operators in Rn, J. Math. Anal. Appl., 42 (1973), pp. 271-301. | MR 320821 | Zbl 0272.35029

[25] V S. RABINOVIč, Pseudo- differential operators on a class of noncompact manifolds, Math. USSR-Sb., 18 (1972), pp. 45-59. | Zbl 0257.58009

[26] G. De Rham, Varieties Differentiables, 3rd ed., Hermann, Paris, 1973. | Zbl 0284.58001

[27] R. Seeley, Singular integrals and boundary value problems, Amer. J. Math., 88 (1966), pp. 781-809. | MR 209915 | Zbl 0178.17601

[28] L.A. Bagirov - V.A. Kondrat'Ev, Elliptic equations in Rn, Differential Equations, 11 (1975), pp. 375-379. | MR 377270 | Zbl 0331.35021