Skip to content
GJMA Global Journal of Mathematical Analysis E-ISSN 2307-9002

The Cauchy problem and Hadamard's example

Abstract

Integral representation for harmonic function  in the ring. We prove the existence and uniqueness of solutions of the Cauchy problem for the Laplace equation in the circle. Integral representation for the solution of the Cauchy problem was found.

Authors and Affiliations

About this article

Download PDF

References

[1] Lavrentev M.M., Romanov V.G. and Shishatskii S.P., ”Ill-Posed Problems of Mathematical Physics and Analysis.”, American Mathematical Society, Providence,, (1986).

[2] Lavrentev M.M., Reznitskay K.G., Yakhno V.G., ”One-Dimensional Inverse Problems of Mathematical Physics.”,American Mathematical Society Translations, Series 2, Vol. 130, (1986).

[3] Nikol’skii, S.M. ,Sobolev space, in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104,(2001).

[4] A.N. Tychonov, V. Y. Arsenin , ”Solution of Ill-posed Problems.”,Washington: Winston and Sons. ISBN 0-470-99124-0(1977).

[5] Lavrentev M.A., Shabat B.V., ”Metods of Theory of Functions of a Complex Variable (in Russian)”,Nauka, Moscow,(1973).

View more references (1)

[6] Ahlfors, Lars (1979), Complex analysis (3rd ed.), McGraw Hill, ISBN 978-0070006577.


How to Cite

Yaremko, O., & Mogileva, E. S. (2013). The Cauchy problem and Hadamard’s example. Global Journal of Mathematical Analysis, 1(2), 48-52. https://doi.org/10.14419/gjma.v1i2.876