What is it about?
Using a hypercomplex analog of the Cauchy type integral, we reduce the BVP-problem for hypercomplex monigenic functions with values on 2-D commutative algebra to a system of integral equations on the real axes. We establish sufficient conditions under which this system has the Fredholm property and the unique solution. A displacements-type boundary value problem of 2-D isotropic elasticity theory is reduced to this BVP problem with appropriate boundary conditions.
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Why is it important?
A displacements-type boundary value problem of 2-D isotropic elasticity theory is reduced to this BVP problem for monogenic functions with appropriate boundary conditions.
Perspectives
It gives an advantage to Elasticity Theory.
Serhii Gryshchuk
Institute of Mathematics of the National Academy of Ukraine
Read the Original
This page is a summary of: Reduction of a Schwartz-type boundary value problem for biharmonic monogenic functions to Fredholm integral equations, Open Mathematics, April 2017, De Gruyter,
DOI: 10.1515/math-2017-0025.
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