Abstract
Theorems of the Phragmén–Lindelöf type for biharmonic functions, which is obtained using Carleman type formulas, is considered.
REFERENCES
M. A. Evgrafov and I. A. Chegis, “Generalization of the Phragmén–Lindelöf theorem on analytic functions to harmonic functions in space,” Dokl. Akad. Nauk SSSR 134 (2), 259–262 (1960).
I. A. Chegis, “A Phragmén–Lindelöf type theorem for functions harmonic in a rectangular cylinder,” Dokl. Akad. Nauk SSSR 136 (3), 556–559 (1961).
I. S. Arshon and M. A. Evgrafov, “On the growth of functions harmonic in a cylinder and bounded on its surface together with the normal derivative,” Dokl. Akad. Nauk SSSR 142 (4), 762–765 (1962).
I. S. Arshon and M. A. Evgrafov, “An example of a function harmonic in the whole space and bounded outside a circular cylinder,” Dokl. Akad. Nauk SSSR 143 (1), 9–10 (1962).
I. S. Arshon and M. A. Evgrafov, “On the growth of harmonic functions of three variables,” Dokl. Akad. Nauk SSSR 147 (4), 755–757 (1962).
A. F. Leon’tev, “Theorems of Phragmén–Lindelöf type for harmonic functions in a cylinder,” Izv. Akad. Nauk SSSR Ser. Mat. 27 (3), 661–676 (1963).
Sh. Yarmukhamedov, “The Cauchy problem for a polyharmonic equation,” Dokl. Akad. Nauk 388 (2), 162–165 (2003).
Z. R. Ashurova, N. Yu. Jurayeva, and U. Yu. Jurayeva, “On some properties of the Yarmukhamedov kernel,” Int. J. Innovative Res. Sci. Eng. Technol. 10 (6), 7338–7341 (2021).
N. Yu. Jurayeva, Z. R. Ashurova, and U. Yu. Jurayeva, “Growing polyharmonic functions and the Cauchy problem,” J. Crit. Rev. 7 (7), 371–378 (2020). https://doi.org/10.31838/jcr.07.07.62
Z. R. Ashurova, N. Yu. Jurayeva, and U. Yu. Jurayeva, “Task Cauchy and Carleman function,” Academicia: Int. Multidiscip. Res. J. 10 (5), 1784–1789 (2020). https://doi.org/10.5958/2249-7137.2020.00369.9
G. M. Goluzin and V. I. Krylov, “The generalized Carleman formula and its application to the analytic continuation of functions,” Mat. Sb. 40 (2), 144–149 (1933).
A. N. Tikhonov, “On the stability of inverse problems,” Dokl. Akad. Nauk SSSR 39 (5), 195–198 (1943).
M. M. Lavrent’ev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems of Mathematical Physics and Analysis (Nauka, Moscow, 1980) [in Russian].
Sh. Yarmukhamedov, “A Green formula in an infinite domain and its application,” Dokl. Akad. Nauk SSSR 285 (2), 305–308 (1985).
Z. R. Ashurova, “Phragmén–Lindelöf type theorems for harmonic functions of several variables,” Akad. Nauk Uzb. SSR 5, 6–8 (1990).
N. Yu. Jurayeva, U. Yu. Jurayeva, and U. M. Saidov, “A Carleman function for polyharmonic functions for some domains lying in m-dimensional even Euclidean space,” Uzbek Math. J., No. 3, 92–97 (2011).
A. B. Khasanov and F. R. Tursunov, “On Cauchy problem for Laplace equation,” Ufa Math. J. 11 (4), 91–107 (2019). https://doi.org/10.13108/2019-11-4-91
A. B. Khasanov and F. R. Tursunov, “On the Cauchy problem for the three-dimensional Laplace equation,” Russ. Math. 65 (2), 49–64 (2021). https://doi.org/10.3103/S1066369X21020055
I. N. Vekua, “Complex representation of solutions of elliptic differential equations and its applications to boundary value problems,” Tr. Tbilis. Mat. Inst. 7, 161–173 (1939).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declares that she has no conflicts of interest.
Additional information
Translated by M. Talacheva
About this article
Cite this article
Jurayeva, U.Y. Theorems of the Phragmén–Lindelöf Type for Biharmonic Functions. Russ Math. 66, 33–55 (2022). https://doi.org/10.3103/S1066369X22100097
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X22100097