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Discrete Hölder estimates for a parametrix variation

Abstract

In nonhomogeneous Hölder spaces, we prove continuity of integral operators with kernels from a special class and indicate simplest properties of this class. A parametrix of new type is constructed in a half-space for second order elliptic operators. We establish that, in local Hölder norms, it admits more exact estimate than that for a parametrix close to the Levi function.

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Correspondence to A. I. Parfenov.

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Original Russian Text © A.I. Parfenov, 2014, published in Matematicheskie Trudy, 2014, Vol. 17, No. 1, pp. 175–201.

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Parfenov, A.I. Discrete Hölder estimates for a parametrix variation. Sib. Adv. Math. 25, 209–229 (2015). https://doi.org/10.3103/S1055134415030062

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Keywords

  • Hölder space
  • integral operator
  • parametrix
  • discretization
  • stability of the Green functions