Extension properties and boundary estimates for a fractional heat operator. (July 2016)

• Record Type: Journal Article
• Authors: Nyström, K.; Sande, O.
• Is Part Of: Nonlinear analysis. Volume 140(2016)
• Page Start: 29
• Page End: 37
• Publication Date: 2016-07
• Subjects: Fractional Laplacian -- Fractional heat equation -- Dirichlet to Neumann map -- Parabolic integro-differential equations -- Linear degenerate parabolic equation -- Lipschitz domain -- Boundary Harnack inequality; 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.2016.02.027
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The square root of the heat operator ∂ t − Δ, can be realized as the Dirichlet to Neumann map of the heat extension of data on R n + 1 to R + n + 2 . In this note we obtain similar characterizations for general fractional powers of the heat operator, ( ∂ t − Δ ) s, s ∈ ( 0, 1 ) . Using the characterizations we derive properties and boundary estimates for parabolic integro-differential equations from purely local arguments in the extension problem.