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Riemann-Hilbert problem on an elliptic surface and a uniformly stressed inclusion embedded into a half-plane subjected to antiplane strain
Y. A. Antipov
An inverse problem of elasticity of elastic inclusions embedded into an elastic half-plane is analyzed. The boundary of the half-plane is free of traction. The half-plane and t…
Sadovskii vortex in a wedge and the associated Riemann-Hilbert problem on a torus
Y. A. Antipov, A. Y. Zemlyanova
Reconstruction of conformal mappings from canonical slit domains onto multiply-connected physical domains with a free boundary is of interest in many different models arising in fl…
Integral relations associated with the semi-infinite Hilbert transform and applications to singular integral equations
Y. A. Antipov, S. M. Mkhitaryan
Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of t…
Method of automorphic functions for an inverse problem of antiplane elasticity
Y. A. Antipov
A nonlinear inverse problem of antiplane elasticity for a multiply connected domain is examined. It is required to determine the profile of uniformly stressed inclusions when t…
The Generalized Mader's Inversion Formulas for the Radon Transforms
Yuri A. Antipov, Boris Rubin
In 1927 Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on $\bbr^n$. These formulas differ from the original ones by Radon and seem to be forg…