Electron. J. Differential Equations, Vol. 2023 (2023), No. 67, pp. 1-14.

Boundedness on generalized Morrey spaces for the Schrodinger operator with potential in a reverse Holder class

Guiyun Wang, Shenzhou Zheng

Abstract:
In this article, we prove boundedness for the Hessian of a Schrodinger operator with weak regularity on the coefficients, and potentials satisfying the reverse Holder condition. This is done in in generalized Morrey spaces, and in vanishing generalized Morrey spaces. On the Schrodinger operator L=−aij(x)Dij+V(x) it is assumed that aij∈BMOθ(ρ) (a generalized Morrey space) and that V(x)∈Bn/2∗ (a reverse Holder class).

Submitted May 29, 2023. Published October 13, 2023.
Math Subject Classifications: 35J10, 42B35, 42B20.
Key Words: Schrodinger operators; reverse Holder class; generalized Morrey space; vanishing generalized Morrey space; BMO-theta-rho coefficients.
DOI: 10.58997/ejde.2023.67

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Guiyun Wang
Mathematics teaching and research group
Zhejiang Institute of Communications
Hangzhou 311112, China
email: 154621582@qq.com
Shenzhou Zheng
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: shzhzheng@bjtu.edu.cn

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