OPTIMAL METHODS OF LAPLACIAN FIELD REGENERATION 

Boykov Ilya Vladimirovich, Doctor of Science (in Mathematics), professor, head of sub-department of highest and applied mathematics, Penza State University
Kravchenko Marina Vitalyevna, graduate student, Penza State University

550.831

In the paper considered optimal with respect to accuracy methods for approximation Laplace vector fields. For this purpuse the smooth Laplace vector fields is investigated. Introduced the new functional class B_α,1(Ω,M), Ω=-1,1]^l, l =1,2…, M=const. Evaluated Kolmogorov widths and Babenko widths for this class of functions. Constructed  local splines and shown that this splines are optimal with respect to accuracy methods for approximation Laplace fields.

Laplase vector fields, elliptic equations, spline, Kolmogorov and Babenko widths, direct problems of gravity.