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.