2019/01/17 by S. V. Gryshchuk, Serhii V. Gryshchuk, Gryshchuk, Serhii V.
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #Primary 30G35 #Secondary 74B05 #math.AP #msc:30G35 #msc:74B05
paper · pdf · doi:10.48550/arxiv.1901.05882
arxiv created 2019/01/17 · openalex publication_date 2019/01/17 · arxiv updated 2019/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A solution of the elliptic type PDE of the 4th order, being a reduction of the Eqs. of stress function corresponding to any case of plane anisotropy which is not equal to isotropy (proved by S. G.~Mikhlin), is described in terms of hypercomplex `analytic' functions with values in two-dimensional semisimple algebra over the field of complex numbers in case when a domain under consideration is bounded and simply-connected. A boundary value problem on finding a function which satisfies this PDE in the considered domain (bounded and simply-connected) and permits continuations (to the boundary) of operators (∂)/(∂ x) and (∂)/(∂ y) acted to it, is reduced to certain BVP for these hypercomplex functions.