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
MathSciNet review:
741733
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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 (84m:58136)

[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
(89m:58193), http://dx.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 (82d:81074)

Peter
Greiner, An asymptotic expansion for the heat equation, Arch.
Rational Mech. Anal. 41 (1971), 163–218. MR 0331441
(48 #9774)

Peter
D. Lax, Asymptotic solutions of oscillatory initial value
problems, Duke Math. J. 24 (1957), 627–646. MR 0097628
(20 #4096)

[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
(84i:35113), http://dx.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
(85e:46002)

[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
(83a:58085), http://dx.doi.org/10.1002/cpa.3160350104
 [Cl] C. Callias, The heat equation with singular coefficients. I, Comm. Math. Phys. 88 (1983), 357385. MR 701923
 [C2] C. Callias, Asymptotics of the heat kernel for Schrödinger operators with isolated singularities in the coefficients, 1982 (preprint).
 [C3] C. Callias, The resolvent and the heat kernel for some singular boundary problems, 1983 (preprint). MR 946284
 [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.
 [CT] C. Callias and C. Taubes, Functional determinants in Euclidean YangMills theory, Comm. Math. Phys. 77 (1980), 229250. 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.
 [Ph] R. Phillips, Scattering theory for the wave equation with a short range perturbation, Indiana Univ. Math. J. 31 (1982), 609639. MR 667785
 [RS] M. Reed and B. Simon, Methods of modern mathematical physics, Vol. 11, Academic Press, New York, 1975. MR 751959
 [S] R. Seeley, Asymptotics of certain integrals of symbols, 1983 (preprint).
 [U] G. Uhlmann, Light intensity distribution in conical refraction, Comm. Pure Appl. Math. 35 (1982), 6980. MR 637495
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Additional Information
DOI:
http://dx.doi.org/10.1090/S027309791984152558
PII:
S 02730979(1984)152558
