Nonlocal Harnack inequalities for nonlocal heat equations

2018/03/28 by Yong‐Cheol Kim, Kim, Yong-Cheol · 1 citation
Computer Science · Mathematics · #35B65 #35D10 (60J75) #35J60 #45K05 #47G20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1804.00534

openalex publication_date 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, applying the De Giorgi method, we obtain nonlocal Harnack inequalities for weak solutions of nonlocal parabolic equations given by an integro-differential operator \rL_K as follows; \begincases \rL_K u+\pa_t u=0 amp; in \Om×(-T,0] u=g amp;\text in ((\BRⁿ\s\Om)× (-T,0])∪(\Om×\t=-T\) \endcases where g∈ C(\BRⁿ× [-T,0])∩ L^\iy(\BRⁿ×(-T,0]) and \Om is a bounded domain in \BRⁿ with Lipschitz boundary. Moreover, we get nonlocal parabolic weak Harnack inequalities of the weak solutions.

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