Doob's ω-Transform on Local Dirichlet Spaces. (23rd August 2021)

• Record Type: Journal Article
• Authors: Bezzarga, Mounir; Kenzizi, Tarek
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 12(2021)
• Page Start: 1423
• Page End: 1443
• Publication Date: 2021-08-23
• Subjects: Dirichlet forms -- heat equation -- parabolic problem; 35J35 -- 35J50 -- 35J60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1962909
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we study the existence and uniqueness of nonnegative solutions for the following parabolic problem { H t ω u + ∂ u ∂ t = 0, in X × ( 0, T ), u ( x, 0 ) = u 0 ( x ), in X, where T > 0, X is a locally compact separable metric space, Ht is a operator (not necessarily selfadjoint) associated with a regular (not necessarily symmetric)local Dirichlet form E t, the initial value u 0 ∈ L 2 ( X, ω 2 d m ) and m is a positive Radon measure on Borel subset U of X such that m ( U ) > 0. Our technical approach for uniqueness is based on Täcklind type uniqueness theorem.