A method for the construction of reflection laws for a parabolic equation
Author:
C. Denson Hill
Journal:
Trans. Amer. Math. Soc. 133 (1968), 357-372
MSC:
Primary 35.62
DOI:
https://doi.org/10.1090/S0002-9947-1968-0235287-8
MathSciNet review:
0235287
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References | Similar Articles | Additional Information
- R. J. Duffin, Continuation of biharmonic functions by reflection, Duke Math. J. 22 (1955), 313–324. MR 79105
- Vladimir Filippenko, On the reflection of harmonic functions and of solutions of the wave equation, Pacific J. Math. 14 (1964), 883–893. MR 170105
- P. R. Garabedian, Partial differential equations with more than two independent variables in the complex domain, J. Math. Mech. 9 (1960), 241–271. MR 0120441, DOI https://doi.org/10.1512/iumj.1960.9.59015
- P. R. Garabedian, Analyticity and reflection for plane elliptic systems, Comm. Pure Appl. Math. 14 (1961), 315–322. MR 136848, DOI https://doi.org/10.1002/cpa.3160140311
- P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045 J. Hadamard, Lectures on Cauchy’s problem in linear partial differential equations, Dover, New York, 1952.
- C. Denson Hill, Parabolic equations in one space variable and the non-characteristic Cauchy problem, Comm. Pure Appl. Math. 20 (1967), 619–633. MR 214927, DOI https://doi.org/10.1002/cpa.3160200309
- Alfred Huber, The reflection principle for polyharmonic functions, Pacific J. Math. 5 (1955), 433–439. MR 70736
- Fritz John, Continuation and reflection of solutions of partial differential equations, Bull. Amer. Math. Soc. 63 (1957), 327–344. MR 89332, DOI https://doi.org/10.1090/S0002-9904-1957-10138-4
- Hans Lewy, On the reflection laws of second order differential equations in two independent variables, Bull. Amer. Math. Soc. 65 (1959), 37–58. MR 104048, DOI https://doi.org/10.1090/S0002-9904-1959-10270-6
- Hans Lewy, On the extension of harmonic functions in three variables, J. Math. Mech. 14 (1965), 925–927. MR 0204875
- Hillel Poritsky, Application of analytic functions to two-dimensional biharmonic analysis, Trans. Amer. Math. Soc. 59 (1946), 248–279. MR 15630, DOI https://doi.org/10.1090/S0002-9947-1946-0015630-0
- Arnold Sommerfeld, Partial Differential Equations in Physics, Academic Press, Inc., New York, N. Y., 1949. Translated by Ernst G. Straus. MR 0029463
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Article copyright:
© Copyright 1968
American Mathematical Society