Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Singular asymptotics approach to partial differential equations with isolated singularities in the coefficients

Authors: Constantine J. Callias and Gunther A. Uhlmann
Journal: Bull. Amer. Math. Soc. 11 (1984), 172-176
MSC (1980): Primary 35P25, 35K05, 41A60, 58G99; Secondary 35A30, 35L05, 35R05
MathSciNet review: 741733
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • Constantine J. Callias, The heat equation with singular coefficients. I. Operators of the form -𝑑²/𝑑𝑥²+𝜅/𝑥² in dimension 1, Comm. Math. Phys. 88 (1983), no. 3, 357–385. MR 701923
  • [C2] C. Callias, Asymptotics of the heat kernel for Schrödinger operators with isolated singularities in the coefficients, 1982 (preprint).
  • Constantine J. Callias, The resolvent and the heat kernel for some singular boundary problems, Comm. Partial Differential Equations 13 (1988), no. 9, 1113–1155. MR 946284, 10.1080/03605308808820570
  • [CM] C. Callias and X. Markenscoff, Singular asymptotics of integrals and the near field radaited from a non-uniformly moving dislocation, Ninth U. S. Congress of Applied Mechanics, Cornell Univ., June 1982.
  • Constantine Callias and Clifford H. Taubes, Functional determinants in Euclidean Yang-Mills theory, Comm. Math. Phys. 77 (1980), no. 3, 229–250. MR 594302
  • Peter Greiner, An asymptotic expansion for the heat equation, Arch. Rational Mech. Anal. 41 (1971), 163–218. MR 0331441
  • Peter D. Lax, Asymptotic solutions of oscillatory initial value problems, Duke Math. J. 24 (1957), 627–646. MR 0097628
  • [M] R. B. Melrose, Lectures on scattering theory, M.I.T., 1981.
  • Ralph S. Phillips, Scattering theory for the wave equation with a short range perturbation, Indiana Univ. Math. J. 31 (1982), no. 5, 609–639. MR 667785, 10.1512/iumj.1982.31.31045
  • Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959
  • [S] R. Seeley, Asymptotics of certain integrals of symbols, 1983 (preprint).
  • G. A. Uhlmann, Light intensity distribution in conical refraction, Comm. Pure Appl. Math. 35 (1982), no. 1, 69–80. MR 637495, 10.1002/cpa.3160350104

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 35P25, 35K05, 41A60, 58G99, 35A30, 35L05, 35R05

Retrieve articles in all journals with MSC (1980): 35P25, 35K05, 41A60, 58G99, 35A30, 35L05, 35R05

Additional Information