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**0204861**, https://doi.org/10.1007/BF02414343**2.**David Colton,*Cauchy’s problem for almost linear elliptic equations in two independent variables*, J. Approximation Theory**3**(1970), 66–71. MR**0259347****3.**P. R. Garabedian,*Partial differential equations*, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR**0162045****4.**J. Hadamard,*Lectures on the Cauchy problem in linear partial differential equations*, Yale Univ. Press, New Haven, Conn., 1923.**5.**Peter 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**0085427**, https://doi.org/10.1007/BF01600500**6.**L. E. Payne,*Some general remarks on improperly posed problems for partial differential equations*, Symposium on Non-Well-Posed Problems and Logarithmic Convexity (Heriot-Watt Univ., Edinburgh, 1972) Springer, Berlin, 1973, pp. 1–30. Lecture Notes in Math., Vol. 316. MR**0410142****7.**I. N. Vekua,*Novye metody rešeniya èlliptičeskih uravneniĭ*, OGIZ, Moscow-Leningrad,], 1948 (Russian). MR**0034503****8.**Chung Ling Yu,*Reflection principle for systems of first order elliptic equations with analytic coefficients*, Trans. Amer. Math. Soc.**164**(1972), 489–501. MR**0293110**, https://doi.org/10.1090/S0002-9947-1972-0293110-0**9.**Chung Ling 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**0326162**, https://doi.org/10.1090/S0002-9947-1973-0326162-0**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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Additional Information

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