The existence for the solution of the elliptic Cauchy problem

Author:
Chung-Ling Yu

Journal:
Bull. Amer. Math. Soc. **80** (1974), 545-548

MSC (1970):
Primary 30A92, 30A93, 30A82, 35A20, 33B30, 35G10, 35J60

DOI:
https://doi.org/10.1090/S0002-9904-1974-13490-7

MathSciNet review:
0338553

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References | Similar Articles | Additional Information

**1.**A. K. Aziz, R. P. Gilbert and H. C. Howard,*A second order, non-linear elliptic boundary value problem with generalized Goursat data*, Ann. Mat. Pura Appl. (4) 72 (1966), 325-341. MR 34 #4697. MR**204861****2.**D. Colton,*Cauchy's problem for almost linear elliptic equations in two independent variables*, J. Approximation Theory 3 (1970), 66-71. MR 41 #3985. MR**259347****3.**P. R. Garabedian,*Partial differential equations*, Wiley, New York, 1964. MR 28 #5247. MR**162045****4.**J. Hadamard,*Lectures on the Cauchy problem in linear partial differential equations*, Yale Univ. Press, New Haven, Conn., 1923.**5.**P. Henrici,*A survey of I. N. Vekua's theory of elliptic partial differential equations with analytic coefficients*, Z. Angew. Math. Phys. 8 (1957), 169-203. MR 19, 38. MR**85427****6.**L. E. Payne,*Some remarks on improperly posed problems for partial differential equations*, Lecture Notes in Math., vol. 316, Springer-Verlag, Berlin and New York, 1973, pp. 1-30. MR**410142****7.**I. N. Vekua,*New methods for solving elliptic equations*, OGIZ, Moscow, 1948; English transl., Series in Appl. Math., vol. 1, North-Holland, Amsterdam; Interscience, New York, 1967. MR 11, 598; 35 #3243. MR**34503****8.**C. L. Yu,*Reflection principle for systems of first order elliptic equations with analytic coefficients*, Trans. Amer. Math. Soc. 164 (1972), 489-501. MR 45 #2189. MR**293110****9.**C. L. Yu,*Cauchy problem and analytic continuation for systems of first order elliptic equations with analytic coefficients*, Trans. Amer. Math. Soc. 185 (1973), 429-443. MR**326162****10.**C. L. Yu,*Cauchy problem for systems of first order analytic elliptic equations*, SIAM J. Math. Anal. (to appear).**11.**C. L. Yu,*Cauchy problem for a class of higher order analytic elliptic equations*(to appear).**12.**C. L. Yu,*On the global solvability of a linear elliptic Cauchy problem*(to appear).

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DOI:
https://doi.org/10.1090/S0002-9904-1974-13490-7