Local properties for weak solutions of nonlocal heat equations. (March 2020)

• Record Type: Journal Article
• Authors: Kim, Yong-Cheol
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 47G20 -- 45K05 -- 35J60 -- 35B65 -- 35D10 -- 60J75; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111689
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, using the De Giorgi–Nash–Moser theory, we obtain an interior parabolic Hölder regularity for weak solutions of nonlocal heat equations given by an integro-differential operator L K as follows; L K u + ∂ t u = 0 in Ω × ( − T, 0 ] u = g in ( ( R n ∖ Ω ) × ( − T, 0 ] ) ∪ ( Ω × { t = − T } ) where g ∈ C ( R n × [ − T, 0 ] ) ∩ L ∞ ( R n × ( − T, 0 ] ) ∩ H T s ( R n ) and Ω ⊂ R n is a bounded domain with Lipschitz boundary. In addition, we get the local boundedness of such weak solutions.