The Harnack inequality for a class of nonlocal parabolic equations-Reference-Cited by-同舟云学术

The Harnack inequality for a class of nonlocal parabolic equations

Published:2020-09-03 Issue:06 Volume:23 Page:2050050
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Banerjee Agnid¹,Garofalo Nicola²,Munive Isidro H.³,Nhieu Duy-Minh⁴

Affiliation:

1. TIFR CAM, Bangalore 560065, India

2. Dipartimento di Ingegneria Civile, Edile e Ambientale (DICEA), Università di Padova, Padova 35131, Italy

3. Department of Mathematics, University Center of Exact Sciences and Engineering, University of Guadalajara, Guadalajara 44430, Mexico

4. Department of Mathematics, National Central University, Zhongli District, Taoyuan city 32001, Taiwan, ROC

Abstract

In this paper, we establish a scale invariant Harnack inequality for the fractional powers of parabolic operators [Formula: see text], [Formula: see text], where [Formula: see text] is the infinitesimal generator of a class of symmetric semigroups. As a by-product, we also obtain a similar result for the nonlocal operators [Formula: see text]. Our focus is on non-Euclidean situations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199720500509

Reference39 articles.

1. Fractional powers of closed operators and the semigroups generated by them

2. Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations

3. A Saint-Venant type principle for Dirichlet forms on discontinuous media

4. The boundary Harnack principle for the fractional Laplacian

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