Regularity of hyperbolic magnetic Schrodinger equation with oscillating coefficients

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Wu, Yanhua¹  Lu, Xiaojun^2,3 

[1] Hohai Univ, Sch Publ Adm, Dept Sociol, Nanjing 211189, Jiangsu, Peoples R China

[2] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China

[3] Southeast Univ, Jiangsu Key Lab Engn Mech, Nanjing 210096, Jiangsu, Peoples R China

关键词: Hyperbolic magnetic Schrodinger equation;    Loss of regularity;    Optimality of regularity;    Microlocal analysis;    Instability arguments;   

DOI  :  10.1016/j.jde.2017.03.037

来源: Elsevier

【 摘 要 】

This paper mainly discusses the regularity of hyperbolic magnetic Schrodinger equation with singular coefficients near the origin. We apply the techniques from microlocal analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the result, a delicate counter-example with periodic coefficients will be constructed to show the lower bound of loss of regularity by the application of harmonic analysis and instability arguments. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free