Dirichlet problem for Schrodinger equation with the boundary value in the BMO space

作     者：Renjin Jiang Bo Li Renjin Jiang;Bo Li

作者机构：Center for Applied MathematicsTianjin UniversityTianjin 300072China College of Data ScienceJiaxing UniversityJiaxing 314001China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2022年第65卷第7期

页      面：1431-1468页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11922114 11671039 and 11771043)。 

主　　题：Schrodinger equation BMO Carleson measure metric measure space 

摘      要：Let(X,d,μ)be a metric measure space satisfying a Q-doubling condition(Q1)and an L^(2)-Poincaréinequality.Let L=L+V be a Schrödinger operator on X,where L is a non-negative operator generalized by a Dirichlet form,and V is a non-negative Muckenhoupt weight that satisfies a reverse Hölder condition RH_(q) for some q≥(Q+1)/2.We show that a solution to(L−∂_(t)^(2))u=0 on X×R_(+) satisfies the Carleson condition,sup_(B(xB,rB))1/μ(B(xB,rB))∫_(0)^(rB)∫_(B(xB,rB))|t∇u(x,t)|^(2)dμdt/t∞if and only if u can be represented as the Poisson integral of the Schrodinger operator L with the tracein the BMO(bounded mean oscillation)space associated with L.