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- W2031240166 abstract "This paper studies the third problem for the Laplace equation on a bounded planar domain with inside cracks. The third condition<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi></mml:math>is given on the boundary of the domain. The skip of the function<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>u</mml:mi><mml:mo>+</mml:mo></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mo>−</mml:mo></mml:msub><mml:mo>=</mml:mo><mml:mi>g</mml:mi></mml:math>and the modified skip of the normal derivatives<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo></mml:msub><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mo>+</mml:mo></mml:msub><mml:mo>=</mml:mo><mml:mi>f</mml:mi></mml:math>are given on cracks. The solution is looked for in the form of the sum of a modified single-layer potential and a double-layer potential. The solution of the corresponding integral equation is constructed." @default.
- W2031240166 created "2016-06-24" @default.
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- W2031240166 date "2006-01-01" @default.
- W2031240166 modified "2023-10-17" @default.
- W2031240166 title "The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks" @default.
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- W2031240166 doi "https://doi.org/10.1155/ijmms/2006/91983" @default.
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