Shirokova, E. A. Application of Fredholm integral equations to the investigation of inner inverse boundary value problems. (Russian) Zbl 0574.35077 Tr. Semin. Kraevym Zadacham 21, 233-239 (1984). 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 Cited in 1 Document 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 Keywords:inner inverse boundary value problems; Fredholm integral equation; Tricomi estimates PDFBibTeX XMLCite \textit{E. A. Shirokova}, Tr. Semin. Kraev. Zadacham 21, 233--239 (1984; Zbl 0574.35077) Full Text: EuDML