Abstract
We study a special discrete boundary value problem for a digital elliptic pseudo-differential operator in a discrete quadrant. Using a special periodic wave factorization for a symbol of the pseudo-differential operator we can construct a general solution of the pseudo-differential equation and then to choose appropriate boundary conditions for its unique solvability in corresponding Sobolev–Slobodetskii spaces. We also give a comparison between discrete and continuous solutions for boundary value problems under consideration.
This is a preview of subscription content, log in via an institution to check access.
REFERENCES
A. Samarskii, The Theory of Difference Schemes (CRC, Boca Raton, 2001).
V. Ryaben’kii, Method of Difference Potentials and its Applications (Springer, Berlin, 2002).
A. V. Vasilyev and V. B. Vasilyev, ‘‘Pseudo-differential operators and equations in a discrete half-space,’’ Math. Model. Anal. 23, 492–506 (2018).
V. Vladimirov, Generalized Functions in Mathematical Physics (Mir, Moscow, 1979).
A. Vasilyev and V. Vasilyev, ‘‘Discrete singular operators and equations in a half-space,’’ Azerb. J. Math. 3, 84–93 (2013).
F. Gakhov, Boundary Value Problems (Dover, Mineola, 1981).
N. Muskhelishvili, Singular Integral Equations (North-Holland, Amsterdam, 1976).
V. B. Vasil’ev, Wave Factorization of Elliptic Symbols: Theory and Applications (Kluwer Academic, Dordrecht, 2000).
V. B. Vasil’ev, ‘‘On some new boundary value problems in nonsmooth domains,’’ J. Math. Sci. 173, 225–230 (2011).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by A. B. Muravnik)
Rights and permissions
About this article
Cite this article
Afanasieva, E.B., Khodyreva, A.A. & Vasilyev, V.B. On a Discrete Boundary Value Problem in a Quarter-Plane. Lobachevskii J Math 44, 3191–3196 (2023). https://doi.org/10.1134/S1995080223080024
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080223080024