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Application of Fredholm integral equations to the investigation of inner inverse boundary value problems. (Russian) Zbl 0574.35077

A new method for the investigation and solution of inner inverse boundary value problems for a parameter s being the length of the arc of the unknown contour \(L_ z\) is suggested, which is based on the solution of a Fredholm integral equation with respect to \(\vartheta\) ’(s). \(\vartheta\) (s) is defined by \(\vartheta (s)=\arg (dz/dw)|_{w\in L_ w}.\) By means of Tricomi estimates sufficient criteria for the simplicity of the unknown contour \(L_ z\) are proved, which depend on the initial conditions of the problem considered.
Reviewer: K.Barckow

MSC:

35R30 Inverse problems for PDEs
45B05 Fredholm integral equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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