Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, and Xicheng Zhang. "Heat kernel estimates for critical fractional diffusion operators." Studia Mathematica 224.3 (2014): 221-263. <http://eudml.org/doc/285751>.

@article{LongjieXie2014,
abstract = {We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.},
author = {Longjie Xie, Xicheng Zhang},
journal = {Studia Mathematica},
keywords = {heat kernel estimate; gradient estimate; critical diffusion operator; Levi's method},
language = {eng},
number = {3},
pages = {221-263},
title = {Heat kernel estimates for critical fractional diffusion operators},
url = {http://eudml.org/doc/285751},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Longjie Xie
AU - Xicheng Zhang
TI - Heat kernel estimates for critical fractional diffusion operators
JO - Studia Mathematica
PY - 2014
VL - 224
IS - 3
SP - 221
EP - 263
AB - We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.
LA - eng
KW - heat kernel estimate; gradient estimate; critical diffusion operator; Levi's method
UR - http://eudml.org/doc/285751
ER -