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- W2071464226 abstract "We study the Dirichlet problem for the equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi mathvariant=normal>Δ</mml:mi><mml:mi>u</mml:mi><mml:mo>−</mml:mo><mml:msup><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>in the exterior of nonclosed Lipschitz surfaces in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math>. The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable." @default.
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- W2071464226 date "2013-01-01" @default.
- W2071464226 modified "2023-10-14" @default.
- W2071464226 title "The Dirichlet Problem for the EquationΔu−k2u=0in the Exterior of Nonclosed Lipschitz Surfaces" @default.
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- W2071464226 doi "https://doi.org/10.1155/2013/302628" @default.
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