Dicrete H\"older estimates for a certain kind of parametrix. II
Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 62-91
Voir la notice de l'article provenant de la source Math-Net.Ru
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 Hölder 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 Hölder 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.
Keywords:
cubic discretization, Lipschitz domain, local Hölder norms, parametrix, potential, straightening.
@article{UFA_2017_9_2_a5,
author = {A. I. Parfenov},
title = {Dicrete {H\"older} estimates for a certain kind of parametrix. {II}},
journal = {Ufa mathematical journal},
pages = {62--91},
publisher = {mathdoc},
volume = {9},
number = {2},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a5/}
}
A. I. Parfenov. Dicrete H\"older estimates for a certain kind of parametrix. II. Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 62-91. http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a5/