On solvability of polyharmonic Dirichlet problem in symmetric Sobolev spaces

被引：0

作者：

Bilalov, Bilal T. ^{[1
,2
,3
,6
]}

Sadigova, Sabina R. ^{[1
,4
]}

Sezer, Yonca ^{[2
]}

Nasibova, Natavan P. ^{[5
]}

机构：

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

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

[3] Azerbaijan Univ Architecture & Construct, Dept Funct Anal & Applicat, Baku, Azerbaijan

[4] Khazar Univ, Dept Math, Baku, Azerbaijan

[5] Azerbaijan State Oil & Ind Univ, Dept Gen & Appl Math, Baku, Azerbaijan

[6] Minist Sci & Educ, Inst Math & Mech, Baku, Azerbaijan

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 18期

关键词：

Dirichlet problem; polyharmonic equation; solvability; symmetric Sobolev spaces; ORDER ELLIPTIC-EQUATIONS; MORREY SPACES; ORLICZ SPACES; REGULARITY; BOUNDARY; INDEXES;

D O I：

10.1002/mma.10279

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Omega subset of R-n be a bounded domain with sufficiently smooth boundary partial derivative Omega and X (Omega) be a symmetric space defined on the measure space (Omega; dx). We consider a Dirichlet problem for 2m-th order polyharmonic equation, and we establish its solvability (in strong sense) in Sobolev space W-X(2m) (Omega) generated by the norm of X (Omega). Such spaces include classical Sobolev spaces, Orlicz-Sobolev spaces, grand Sobolev spaces, and Marcinkiewicz-Sobolev spaces. The obtained results are new for these special cases, too.

引用

页码：14386 / 14401

页数：16

共 38 条

[1] ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1.
AGMON, S
DOUGLIS, A
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1959, 12 (04) : 623 - 727
[2] [Anonymous], 1971, Nonhomogeneous boundary value problems and their applications
[3] Bennett Colin, 1988, Interpolation of Operators
[4] Bers L., 1979, PARTIAL DIFFERENTIAL, P343
[5] The Method of Boundary Value Problems in the Study of the Basis Properties of Perturbed System of Exponents in Banach Function Spaces
Bilalov, B. T.
Sadigova, S. R.
Alili, V. G.
[J]. COMPUTATIONAL METHODS AND FUNCTION THEORY, 2024, 24 (01) : 101 - 120
[6] Bilalov BT, 2022, AZERBAIJAN J MATH, V12, P190
[7] The Concept of a Trace and the Boundedness of the Trace Operator in Banach-Sobolev Function Spaces
Bilalov, B. T.
Sadigova, S. R.
Cetin, Seyma
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2022, 43 (09) : 1069 - 1094
[8] ON LOCAL SOLVABILITY OF HIGHER ORDER ELLIPTIC EQUATIONS IN REARRANGEMENT INVARIANT SPACES
Bilalov, B. T.
Sadigova, C. R.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2022, 63 (03) : 425 - 437
[9] On solvability in the small of higher order elliptic equations in grand-Sobolev spaces
Bilalov, B. T.
Sadigova, S. R.
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2021, 66 (12) : 2117 - 2130
[10] Bilalov B. T., 2022, SOME SOLVABILITY PRO

← 1 2 3 4 →