Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Green’s formulas for cone differential operators
HTML articles powered by AMS MathViewer

by Ingo Witt PDF
Trans. Amer. Math. Soc. 359 (2007), 5669-5696 Request permission

Abstract:

Green’s formulas for elliptic cone differential operators are established. This is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint; thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green’s formulas are deduced.
References
  • Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
  • S. Coriasco, E. Schrohe, and J. Seiler, Differential operators on conic manifolds: maximal regularity and parabolic equations, Bull. Soc. Roy. Sci. Liège 70 (2001), no. 4-6, 207–229 (2002). Hommage à Pascal Laubin. MR 1904055
  • J.B. Gil, T. Krainer, and G.A. Mendoza, Geometry and spectra of closed extensions of elliptic cone operators, to appear in Canadian J. Math.
  • Juan B. Gil and Gerardo A. Mendoza, Adjoints of elliptic cone operators, Amer. J. Math. 125 (2003), no. 2, 357–408. MR 1963689, DOI 10.1353/ajm.2003.0012
  • I. C. Gohberg and E. I. Sigal, An operator generalization of the logarithmic residue theorem and Rouché’s theorem, Mat. Sb. (N.S.) 84(126) (1971), 607–629 (Russian). MR 0313856
  • P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol. 24, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 775683
  • M.V. Keldysh, On the eigenvalues and eigenfunctions of certain classes of non-selfadjoint linear operators, Dokl. Akad. Nauk SSSR 77 (1951), 11–14, In Russian.
  • V. A. Kondrat′ev, Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Moskov. Mat. Obšč. 16 (1967), 209–292 (Russian). MR 0226187
  • Vladimir Kozlov and Vladimir Maz′ya, Differential equations with operator coefficients with applications to boundary value problems for partial differential equations, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1999. MR 1729870, DOI 10.1007/978-3-662-11555-8
  • Matthias Lesch, Operators of Fuchs type, conical singularities, and asymptotic methods, Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], vol. 136, B. G. Teubner Verlagsgesellschaft mbH, Stuttgart, 1997. MR 1449639
  • J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
  • Xiaochun Liu and Ingo Witt, Asymptotic expansions for bounded solutions to semilinear Fuchsian equations, Doc. Math. 9 (2004), 207–250. MR 2117414
  • Richard B. Melrose, Transformation of boundary problems, Acta Math. 147 (1981), no. 3-4, 149–236. MR 639039, DOI 10.1007/BF02392873
  • Sergey A. Nazarov and Boris A. Plamenevsky, Elliptic problems in domains with piecewise smooth boundaries, De Gruyter Expositions in Mathematics, vol. 13, Walter de Gruyter & Co., Berlin, 1994. MR 1283387, DOI 10.1515/9783110848915.525
  • Stephan Rempel and Bert-Wolfgang Schulze, Asymptotics for elliptic mixed boundary problems, Mathematical Research, vol. 50, Akademie-Verlag, Berlin, 1989. Pseudo-differential and Mellin operators in spaces with conormal singularity. MR 1002573
  • B.-W. Schulze, Pseudo-differential operators on manifolds with singularities, Studies in Mathematics and its Applications, vol. 24, North-Holland Publishing Co., Amsterdam, 1991. MR 1142574
  • Bert-Wolfgang Schulze, Boundary value problems and singular pseudo-differential operators, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1998. MR 1631763
  • Ingo Witt, Explicit algebras with the Leibniz-Mellin translation product, Math. Nachr. 280 (2007), no. 3, 326–337. MR 2292154, DOI 10.1002/mana.200410485
  • Ingo Witt, Asymptotic algebras, Sūrikaisekikenkyūsho K\B{o}kyūroku 1211 (2001), 21–33. Asymptotic analysis and microlocal analysis of PDE (Japanese) (Kyoto, 2000). MR 1874953
  • Ingo Witt, On the factorization of meromorphic Mellin symbols, Parabolicity, Volterra calculus, and conical singularities, Oper. Theory Adv. Appl., vol. 138, Birkhäuser, Basel, 2002, pp. 279–306. MR 1966207
  • Ingo Witt, Local asymptotic types, Manuscripta Math. 115 (2004), no. 1, 1–17. MR 2092773, DOI 10.1007/s00229-004-0478-5
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35J70, 34B05, 41A58
  • Retrieve articles in all journals with MSC (2000): 35J70, 34B05, 41A58
Additional Information
  • Ingo Witt
  • Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
  • Address at time of publication: Mathematical Institute, University of Göttingen, Bunsenstr. 3-5, D-37073 Göttingen, Germany
  • Email: iwitt@uni-math.gwdg.de
  • Received by editor(s): October 26, 2003
  • Received by editor(s) in revised form: April 20, 2005
  • Published electronically: June 25, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 5669-5696
  • MSC (2000): Primary 35J70; Secondary 34B05, 41A58
  • DOI: https://doi.org/10.1090/S0002-9947-07-04082-2
  • MathSciNet review: 2336302