A method for the construction of reflection laws for a parabolic equation
Author:
C. Denson Hill
Journal:
Trans. Amer. Math. Soc. 133 (1968), 357372
MSC:
Primary 35.62
MathSciNet review:
0235287
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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 [1]
 R. J. Duffin, Continuation of biharmonic functions by reflection, Duke Math. J. 22 (1955), 313324. MR 0079105 (18:29e)
 [2]
 V. Filippenko, On the reflection of harmonic functions and of solutions of the wave equation, Pacific J. Math. 14 (1964), 883893. MR 0170105 (30:346)
 [3]
 P. R. Garabedian, Partial differential equations with more than two independent variables in the complex domain, J. Math. Mech. 9 (1960), 241271. MR 0120441 (22:11195)
 [4]
 P. R. Garabedian, Analyticity and reflection for plane elliptic systems, Comm. Pure Appl. Math. 14 (1961), 315322. MR 0136848 (25:309)
 [5]
 , Partial differential equations, Wiley, New York, 1964. MR 0162045 (28:5247)
 [6]
 J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Dover, New York, 1952.
 [7]
 C. D. Hill, Parabolic equations in one space variable and the noncharacteristic Cauchy problem, Comm. Pure Appl. Math. 20 (1967), 619633. MR 0214927 (35:5774)
 [8]
 A. Huber, The reflection principle for polyharmonic functions, Pacific J. Math. 5 (1955), 433439. MR 0070736 (17:28d)
 [9]
 F. John, Continuation and reflection of solutions of partial differential equations, Bull. Amer. Math. Soc. 63 (1957), 327344. MR 0089332 (19:653e)
 [10]
 H. Lewy, On the reflection laws of second order differential equations in two independent variables, Bull. Amer. Math. Soc. 65 (1959), 3758. MR 0104048 (21:2810)
 [11]
 , On the extension of harmonic functions in three variables, J. Math. Mech. 14 (1965), 925927. MR 0204875 (34:4710)
 [12]
 H. Poritsky, Applications of analytic functions to twodimensional biharmonic analysis, Trans. Amer. Math. Soc. 59 (1946), 258. MR 0015630 (7:449b)
 [13]
 A. Sommerfeld, Partial differential equations in physics, Academic Press, New York, 1949. MR 0029463 (10:608b)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947196802352878
PII:
S 00029947(1968)02352878
Article copyright:
© Copyright 1968 American Mathematical Society
