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), 172176
MSC (1980):
Primary 35P25, 35K05, 41A60, 58G99; Secondary 35A30, 35L05, 35R05
DOI:
https://doi.org/10.1090/S027309791984152558
MathSciNet review:
741733
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References  Similar Articles  Additional Information
 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, https://doi.org/10.1080/03605308808820570

[CM] C. Callias and X. Markenscoff, Singular asymptotics of integrals and the near field radaited from a nonuniformly moving dislocation, Ninth U. S. Congress of Applied Mechanics, Cornell Univ., June 1982.
 Constantine Callias and Clifford H. Taubes, Functional determinants in Euclidean YangMills theory, Comm. Math. Phys. 77 (1980), no. 3, 229–250. MR 594302

[Gr] P. Greiner, An asymptotic expansion for the heat equation, Global Analysis, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R. I., 1968, pp. 137146; Arch. Rational Mech. Anal. 41 (1971), 163218. MR 331441

[L] P. D. Lax, Asymptotic solutions of oscillatory initial valued problems, Duke Math. J. 24 (1957), 627646. MR 97628

[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, https://doi.org/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, https://doi.org/10.1002/cpa.3160350104
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Additional Information
DOI:
https://doi.org/10.1090/S027309791984152558