Optimal methods for restoring Laplace fields

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 $\bar{B}_{\alpha,1}(\Omega,M)$, $\Omega[-1,1]^l$, $l=1,2,...$, $M=const$. 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.