Ufa Mathematical Journal
    Volume 8, Number 1, pp. 68-78

    On convergence of polynomial solutions of minimal surface

    Klyachin A.A., Truhlyaeva I.V.


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    In this paper we consider the polynomial approximate solutions of the Dirichlet problem for minimal surface equation. It is shown that under certain conditions on the geometric structure of the domain the absolute values of the gradients of the solutions are bounded as the degree of these polynomials increases. The obtained properties imply the uniform convergence of approximate solutions to the exact solution of the minimal surface equation.