Advances in Nonlinear Analysis (Mar 2020)

Gradient estimates for the fundamental solution of Lévy type operator

  • Liu Wei,
  • Song Renming,
  • Xie Longjie

DOI
https://doi.org/10.1515/anona-2020-0062
Journal volume & issue
Vol. 9, no. 1
pp. 1453 – 1462

Abstract

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We prove a gradient estimate and the Hölder continuity of the gradient for the fundamental solution of a class of α-stable type operators with α ∈ (0, 1), which improve known results in the literature where the condition α > 1/2 is commonly assumed.

Keywords