Fourth order elliptic operator-differential equations with unbounded operator boundary conditions in the Sobolev-type spaces

Boundary value problems

Araz R Aliev¹  Hassan A Zedan²  Elvin S Rzayev²  Eman S Al-Aidarous³ 

[1] Baku State University, Baku, Azerbaijan;Institute of Mathematics and Mechanics of ANAS, Baku, Azerbaijan;King Abdulaziz University, Jeddah, Saudi Arabia

关键词: elliptic operator-differential equations;    unbounded operator boundary conditions;    regular solution;    regular solvability;    the Sobolev-type space;    intermediate derivative operators;    34G10;    35J40;    47A50;    47D03;   

DOI  :  10.1186/s13661-015-0453-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Conditions for well-posed and unique solvability of a non-homogeneous boundary value problem for a class of fourth order elliptic operator-differential equations with an unbounded operator in boundary conditions are found in this work. Note that these solvability conditions are sufficient, and they are expressed only in terms of the properties of operator coefficients of the boundary value problem. Besides, the estimates for the norms of intermediate derivative operators in a Sobolev-type space are obtained, and their close relationship with the solvability conditions is established.

【 授权许可】

CC BY