Geodesic
On the discrete Dirichlet problem in a quarter plane
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 34-46.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider a discrete elliptic pseudodifferential equation in a quadrant and the related discrete Dirichlet boundary-value problem and discuss conditions for the solvability of a discrete boundary-value problem in discrete analogs of the Sobolev–Slobodetsky spaces. We compare discrete solutions with solutions of the corresponding continual boundary-value problem depending on the discretization parameter.
Keywords: discrete pseudodifferential operator, periodic wave factorization, analyticity, solvability, discrete Dirichlet problem. 
@article{INTO_2023_226_a3,
     author = {V. B. Vasilev (Vasilyev) and A. A. Khodyreva},
     title = {On the discrete {Dirichlet} problem in a quarter plane},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {34--46},
     publisher = {mathdoc},
     volume = {226},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_226_a3/}
}
TY  - JOUR
AU  - V. B. Vasilev (Vasilyev)
AU  - A. A. Khodyreva
TI  - On the discrete Dirichlet problem in a quarter plane
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 34
EP  - 46
VL  - 226
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_226_a3/
LA  - ru
ID  - INTO_2023_226_a3
ER  - 
%0 Journal Article
%A V. B. Vasilev (Vasilyev)
%A A. A. Khodyreva
%T On the discrete Dirichlet problem in a quarter plane
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 34-46
%V 226
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_226_a3/
%G ru
%F INTO_2023_226_a3
V. B. Vasilev (Vasilyev); A. A. Khodyreva. On the discrete Dirichlet problem in a quarter plane. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 34-46. http://geodesic.mathdoc.fr/item/INTO_2023_226_a3/

[1] Vasilev A. V., Vasilev V. B., “Periodicheskaya zadacha Rimana i diskretnye uravneniya v svertkakh”, Differ. uravn., 51:5 (2015), 642–649 | DOI | Zbl

[2] Vasilev V. B., Multiplikatory integralov Fure, psevdodifferentsialnye uravneniya, volnovaya faktorizatsiya, kraevye zadachi, KomKniga, M., 2010

[3] Vasilev V. B., Tarasova O. A., “O diskretnykh kraevykh zadachakh i ikh approksimatsionnykh svoistvakh”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 174 (2020), 12–19 | DOI

[4] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR

[5] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977

[6] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR

[7] Rempel Sh., Shultse B. V., Teoriya indeksa ellipticheskikh kraevykh zadach, Mir, M., 1986 | MR

[8] Ryabenkii V. S., Metod raznostnykh potentsialov i ego prilozheniya, Fizmatlit, M., 2002

[9] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989

[10] Frank L. S., “Prostranstva setochnykh funktsii”, Mat. sb., 86:2 (1971), 187-–233 | Zbl

[11] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, Mir, M., 1987

[12] Eskin G. I., Kraevye zadachi dlya ellipticheskikh psevdodifferentsialnykh uravnenii, Nauka, M., 1973 | MR

[13] Botchway L., Kibiti G., Ruzhansky M., “Difference equations and pseudo-differential operators on $\mathbb{Z}^n$”, J. Funct. Anal., 278:11 (2020), 1–41 | DOI | MR

[14] Rabinovich V. S., “Wiener algebra of operators on the lattice $\mu\mathbb Z^n$ depending on the small parameter $\mu > 0$”, Complex Var. Ellipt. Equations., 58:6 (2013), 751–766 | DOI | MR | Zbl

[15] Tarasova O. A., Vasilyev V. B., “To the theory of discrete boundary value problems”, 4Open., 2:17 (2019), 1–7 | MR

[16] Vasilyev A. V., Vasilyev V. B., “Discrete singular operators and equations in a half-space”, Azerb. J. Math., 3:1 (2013), 81–93 | MR

[17] Vasilyev A. V., Vasilyev V. B., “Pseudo-differential operators and equations in a discrete half-space”, Math. Model. Anal., 23:3 (2018), 492–506 | DOI | MR | Zbl

[18] Vasilyev A. V., Vasilyev V. B., “On some discrete potential like operators”, Tatra Mt. Math. Publ., 71 (2018), 195–212 | MR | Zbl

[19] Vasilyev V. B., “The periodic Cauchy kernel, the periodic Bochner kernel, discrete pseudo-differential operators”, AIP Conf. Proc., 1863:1 (2017), 140014 | DOI

[20] Vasilyev V., “Discrete operators in canonical domains”, WSEAS Trans. Math., 16 (2017), 197–201

[21] Vasilyev V. B., “On discrete solutions for pseudo-differential equations”, AIP Conf. Proc., 2116 (2019), 040010 | DOI | MR