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Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain
Science Journal of Applied Mathematics and Statistics
Volume 1, Issue 1, April 2013, Pages: 1-6
Received: Mar. 9, 2013; Published: Apr. 2, 2013
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Aliev Nehan Ali, Baku State University, Baku, Azerbaijan
Abbasova Aygun Khanlar, Baku State University, Baku, Azerbaijan
Zeynalov Ramin M., Institute of Cybernetics of Azerbaijan National Academy of Sciences, Baku, Azerbaijan
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In classic mathematical physics course, under the local boundary conditions the Dirichlet (first kind), Neuman (second kind) and at last special case of Poincare (third kind) boundary value problems were considered for a Laplace equation being a canonic form of elliptic type of equations. Later on for a Laplace equation, under non-local boundary condition the Steklov problem was investigated in [3] and a sufficient condition for Fredholm property was found. Note that here boundary conditions contains non -local and global terms and the investigation method consist of obtaining necessary conditions, regularization of them and reducing the stated boundary problem to the system of second kind Fredholm integral equation with non-singular kernel.
Boundary Value Problem, Local, Non-Local And Global Boundary Condition, Steklov Problem, Necessary Conditions, Regularization, Fredholm Property
To cite this article
Aliev Nehan Ali, Abbasova Aygun Khanlar, Zeynalov Ramin M., Non-local Boundary Condition Steklov Problem for A Laplace Equation in Bounded Domain, Science Journal of Applied Mathematics and Statistics. Vol. 1, No. 1, 2013, pp. 1-6. doi: 10.11648/j.sjams.20130101.11
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