TY - GEN
T1 - Mean value inequalities for jump processes
AU - Chen, Zhen Qing
AU - Kumagai, Takashi
AU - Wang, Jian
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
PY - 2018
Y1 - 2018
N2 - Parabolic Harnack inequalities are one of the most important inequalities in analysis and PDEs, partly because they imply Hölder regularity of the solutions of heat equations. Mean value inequalities play an important role in deriving parabolic Harnack inequalities. In this paper, we first survey the recent results obtained in Chen et al. (Stability of heat kernel estimates for symmetric non-local Dirichlet forms, 2016, [15]; Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms, 2016, [16]) on the study of stability of heat kernel estimates and parabolic Harnack inequalities for symmetric jump processes on general metric measure spaces. We then establish the Lp -mean value inequalities for all p∈ (0, 2] for these processes.
AB - Parabolic Harnack inequalities are one of the most important inequalities in analysis and PDEs, partly because they imply Hölder regularity of the solutions of heat equations. Mean value inequalities play an important role in deriving parabolic Harnack inequalities. In this paper, we first survey the recent results obtained in Chen et al. (Stability of heat kernel estimates for symmetric non-local Dirichlet forms, 2016, [15]; Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms, 2016, [16]) on the study of stability of heat kernel estimates and parabolic Harnack inequalities for symmetric jump processes on general metric measure spaces. We then establish the Lp -mean value inequalities for all p∈ (0, 2] for these processes.
KW - Harnack inequality
KW - Heat kernel estimate
KW - Mean value inequality
KW - Stability
KW - Symmetric jump process
UR - https://www.scopus.com/pages/publications/85049958425
U2 - 10.1007/978-3-319-74929-7_28
DO - 10.1007/978-3-319-74929-7_28
M3 - Conference contribution
AN - SCOPUS:85049958425
SN - 9783319749280
T3 - Springer Proceedings in Mathematics and Statistics
SP - 421
EP - 437
BT - Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
A2 - Trutnau, Gerald
A2 - Eberle, Andreas
A2 - Hoh, Walter
A2 - Kassmann, Moritz
A2 - Grothaus, Martin
A2 - Stannat, Wilhelm
PB - Springer New York LLC
T2 - International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016
Y2 - 10 October 2016 through 14 October 2016
ER -