A Carleman function and the Cauchy problem for the laplace equation

Siberian Mathematical Journal

Volumn 45, Issue 3, 2004, Pages 580-595

  Yarmukhamedov, Sh ^a  

^a NONE

Author keywords

Carleman formula; Carleman function; Fundamental solution; Green's formula; Mittag Leffler entire function; Regularization

Indexed keywords

EID: 3943081984     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:SIMJ.0000028622.69605.c0     Document Type: Article

References (10)

1. Hadamard J., The Cauchy Problem for Linear Partial Differential Equations of Hyperbolic Type [Russian translation], Mir, Moscow (1978).
2. Goluzin G. M. and Krylov V. I., "A generalized Carleman formula and its application to analytic continuation of functions," Mat. Sb., 40, No. 2, 144-149 (1933).
3. Fok V. A. and Kuni F. M., "On the introduction of a 'suppressing' function in dispersion relations," Dokl. Akad. Nauk SSSR, 127, No. 6, 1195-1198 (1959).
4. Lavrent'ev M. M., On Some Ill-Posed Problems of Mathematical Physics [in Russian], Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk (1962).
5. Mergelyan S. N., "Harmonic approximation and approximate solution of the Cauchy problem for the Laplace equation," Uspekhi Mat. Nauk, 11, No. 5, 3-26 (1956).
6. Shlapunov A. A., "On the Cauchy problem for Laplace's equation," Sibirsk. Mat. Zh., 33, No. 3, 205-215 (1992).
7. Dzhrbashyan M. M., Integral Transformations and Representations of Functions in a Complex Domain [in Russian], Nauka, Moscow (1966).
8. Mukhammadzhonov A. M., Yarmukhamedov Sh., and Yarmukhamedov R., "Analytic continuation of sections of a reaction," Teor. i Mat. Fizika, 74, No. 2, 270-280 (1988).
9. Yarmukhamedov Sh., "An analog of the Riemann-Volterra formula for harmonic functions in several variables," Soviet Math. Dokl., 39, No. 3, 560-563 (1989).
10. Yarmukhamedov Sh., "On the Cauchy problem for the Laplace equation in the statement of M. M. Lavrent'ev," in: Ill-Posed Problems of Mathematical Physics and Analysis [in Russian], Nauka, Novosibirsk, 1984, pp. 203-209.