On strong solvability of one nonlocal boundary value problem for Laplace equation in rectangle

被引：0

作者：

Gasymov, Telman ^{[1
,2
]}

Akhmadli, Baharchin ^{[1
]}

Ildiz, Umit ^{[3
]}

机构：

[1] Minist Sci & Educ Azerbaijan, Inst Math & Mech, Dept Nonharmon Anal, Baku, Azerbaijan

[2] Baku State Univ, Dept Theory Funct & Funct Anal, Baku, Azerbaijan

[3] Yildiz Tech Univ, Dept Math, Istanbul, Turkiye

来源：

TURKISH JOURNAL OF MATHEMATICS | 2024年 / 48卷 / 01期

关键词：

Laplace equation; nonlocal problem; weighted Sobolev space; strong solution; ORDER ELLIPTIC-EQUATIONS; LEBESGUE SPACES; EIGENFUNCTIONS; OPERATOR; POINT;

D O I：

10.55730/1300-0098.3489

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

One nonlocal boundary value problem for the Laplace equation in a bounded domain is considered in this work. The concept of a strong solution to this problem is introduced. The correct solvability of this problem in the Sobolev spaces generated by the weighted mixed norm is proved by the Fourier method. In a classic statement, this problem has been earlier considered by E.I.Moiseev [34]. A similar problem has been treated by M.E.Lerner and O.A.Repin [30].

引用

页码：21 / 33

页数：14

共 37 条

[1] LP BEHAVIOR OF EIGENFUNCTION EXPANSIONS [J].

BENZINGE.HE .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 174 (447) :333-344

[2]

Bilalov BT, 2022, AZERBAIJAN J MATH, V12, P190

[3] ON LOCAL SOLVABILITY OF HIGHER ORDER ELLIPTIC EQUATIONS IN REARRANGEMENT INVARIANT SPACES [J].

Bilalov, B. T. ;

Sadigova, C. R. .

SIBERIAN MATHEMATICAL JOURNAL, 2022, 63 (03) :425-437

[4] On solvability in the small of higher order elliptic equations in grand-Sobolev spaces [J].

Bilalov, B. T. ;

Sadigova, S. R. .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2021, 66 (12) :2117-2130

[5] Basis Property of Eigenfunctions in Lebesgue Spaces for a Spectral Problem with a Point of Discontinuity [J].

Bilalov, B. T. ;

Gasymov, T. B. ;

Maharramova, G. V. .

DIFFERENTIAL EQUATIONS, 2019, 55 (12) :1544-1553

[6] A completeness criterion for a double power system with degenerate coefficients [J].

Bilalov, B. T. ;

Guliyeva, F. A. .

SIBERIAN MATHEMATICAL JOURNAL, 2013, 54 (03) :419-424

[7] Solvability in the small of m-th order elliptic equations in weighted grand Sobolev spaces [J].

Bilalov, Bilal ;

Zeren, Yusuf ;

Sadigova, Sabina ;

Cetin, Seyma .

TURKISH JOURNAL OF MATHEMATICS, 2022, 46 (06) :2078-2095

[8] On the fredholmness of the Dirichlet problem for a second-order elliptic equation in grand-Sobolev spaces [J].

Bilalov, Bilal ;

Sadigova, Sabina .

RICERCHE DI MATEMATICA, 2024, 73 (01) :283-322

[9] On the Frame Properties of Degenerate System of Sines [J].

Bilalov, Bilal ;

Guliyeva, Fatima .

JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2012,

[10] Some Remarks on Solvability of Dirichlet Problem for Laplace Equation in Non-standard Function Spaces [J].

Bilalov, Bilal T. ;

Ahmedzadeh, Nigar R. ;

Garayev, Tarlan Z. .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (03)

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