Doob's ω-transform of parabolic problem for fractional Laplacian. Issue 3 (11th February 2023)

• Record Type: Journal Article
• Authors: Bezzarga, Mounir; Kenzizi, Tarek; Nefzi, Chaima
• Is Part Of: Applicable analysis. Volume 102:Issue 3(2023)
• Page Start: 770
• Page End: 781
• Publication Date: 2023-02-11
• Subjects: Fractional Laplacian -- heat equation -- parabolic problem; 35J35 -- 35J50 -- 35J60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1965580
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper studies the existence of nonnegative solutions for the following parabolic problem 1 { L ω u + ∂ u ∂ t = 0, in R d × ( 0, T ), u ( x, 0 ) = u 0 ( x ), in R d, where T >0, L ω is a selfadjoint operator associated with a regular Dirichlet form Q, the initial value u 0 ∈ L 2 ( R d ), u 0 ≥ 0 is a Borel measurable function.