Smoothing and Strichartz estimates for degenerate Schrõdinger-type equations

被引：2
|
作者：
Federico, Serena [1 ,2 ]
Ruzhansky, Michael [1 ,3 ]
机构：
[1] Univ Ghent, Dept Math Anal Logic & Discrete Math, Krijgslaan 281,Bldg S8, B-9000 Ghent, Belgium
[2] Univ Bologna, Dept Math, Piazza Porta San Donato 5, I-40126 Bologna, Italy
[3] Queen Mary Univ London, Sch Math Sci, Mile End Rd, London E1 4NS, England
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 242卷
基金：
英国工程与自然科学研究理事会;
关键词：
Smoothing effect; Strichartz estimates; Variable coefficient Schrodinger operators; Comparison principles; SCHRODINGER-EQUATION; MAGNETIC POTENTIALS; REGULARITY; DECAY; TRANSFORMS; INTEGRALS; OPERATORS;
D O I：
10.1016/j.na.2024.113500
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we focus on the validity of some fundamental estimates for time-degenerate Schrodinger-type operators. On the one hand we derive global homogeneous smoothing estimates for operators of any order by means of suitable comparison principles (that we shall obtain here). On the other hand, we prove weighted Strichartz-type estimates for timedegenerate Schrodinger operators and apply them to the local well-posedness of the semilinear Cauchy problem. Most of our results apply to nondegenerate operators as well, recovering, in these cases, the known standard results.
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页数：19
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