Geodesic
Dicrete Hölder estimates for a certain kind of parametrix. II
Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 62-91 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 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, parametrix, potential, straightening.
Mots-clés : local Hölder norms 
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     title = {Dicrete {H\"older} estimates for a certain kind of parametrix. {II}},
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A. I. Parfenov. Dicrete Hölder 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/

[1] Parfenov A.I., “Diskretnye gelderovy otsenki dlya odnoi raznovidnosti parametriksa”, Matemat. trudy, 17:1 (2014), 175–201 | Zbl

[2] R.A. Hunt, R.L. Wheeden, “Positive harmonic functions on Lipschitz domains”, Trans. Amer. Math. Soc., 147 (1970), 507–527 | DOI | MR | Zbl

[3] D.S. Jerison, C.E. Kenig, “Boundary behavior of harmonic functions in non-tangentially accessible domains”, Adv. Math., 46 (1982), 80–147 | DOI | MR | Zbl

[4] S.E. Warschawski, “On conformal mapping of infinite strips”, Trans. Amer. Math. Soc., 51 (1942), 280–335 | DOI | MR

[5] V. Kozlov, V. Maz'ya, “Asymptotic formula for solutions to elliptic equations near the Lipschitz boundary”, Ann. Mat. Pura Appl. (4), 184 (2005), 185–213 | DOI | MR | Zbl

[6] V. Kozlov, “Asymptotic representation of solutions to the Dirichlet problem for elliptic systems with discontinuous coefficients near the boundary”, Electron. J. Diff. Equ., 2006 (2006), 1–46 | MR

[7] V. Kozlov, “Behavior of solutions to the Dirichlet problem for elliptic systems in convex domains”, Comm. Partial Diff. Equ., 34:1 (2009), 24–51 | DOI | MR | Zbl

[8] K. Ramachandran, “Asymptotic behavior of positive harmonic functions in certain unbounded domains”, Potential Anal., 41:2 (2014), 383–405 | DOI | MR | Zbl

[9] Parfenov A.I., “Vesovaya apriornaya otsenka v raspryamlyaemykh oblastyakh lokalnogo tipa Lyapunova–Dini”, Sibirskie elektr. matemat. izvestiya, 9 (2012), 65–150 | Zbl

[10] Parfenov A.I., “Kriterii raspryamlyaemosti lipshitsevoi poverkhnosti po Lizorkinu–Tribelyu. III”, Matemat. trudy, 13:2 (2010), 139–178 | Zbl