Article

    Ufa Mathematical Journal
    Volume 9, Number 2, pp. 62-91

    Dicrete Holder estimates for a certain kind of parametrix. II


    Parfenov A.I.

    DOI:10.13108/2017-9-2-62

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    In the first paper of this series we have introduced a certain parametrix and the associated potential. The parametrix corresponds to an uniformly elliptic second order differential operator with locally H\"older continuous coefficients in the half-space. Here we show that the potential is an approximate left inverse of the differential operator modulo hyperplane integrals, with the error estimated in terms of the local H\"older norms. As a corollary, we calculate approximately the potential whose density and differential operator originate from the straightening of a special Lipschitz domain. This corollary is meant for the future derivation of approximate formulas for harmonic functions.