HEAT-FLOW MONOTONICITY OF STRICHARTZ NORMS

被引：36

作者：

Bennett, Jonathan ^{[1
]}

Bez, Neal ^{[2
]}

Carbery, Anthony ^{[3
,4
]}

Hundertmark, Dirk ^{[5
,6
]}

机构：

[1] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

[2] Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland

[3] Univ Edinburgh, Sch Math, Edinburgh EH3 9JZ, Midlothian, Scotland

[4] Univ Edinburgh, Maxwell Inst Math Sci, Edinburgh EH3 9JZ, Midlothian, Scotland

[5] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[6] Univ Illinois, Inst Condensed Matter Theory, Urbana, IL 61801 USA

来源：

ANALYSIS & PDE | 2009年 / 2卷 / 02期

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会;

关键词：

heat flow; Strichartz estimates; Schrodinger equation; BRASCAMP-LIEB INEQUALITIES; RESTRICTION;

D O I：

10.2140/apde.2009.2.147

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our main result is that for d = 1, 2 the classical Strichartz norm parallel to e(is Delta) f parallel to(2+4/d)(Ls,x)(RxR(d)) associated to the free Schrodinger equation in nondecreasing as the initial datum f evolves under a certain quadratic heat flow.

引用

页码：147 / 158

页数：12

共 14 条

[1] BALL K, 1989, LECT NOTES MATH, V1376, P251
[2] Barthe F, 2004, LECT NOTES MATH, V1850, P65
[3] BENNETT JM, 2009, B LONDON MA IN PRESS
[4] The Brascamp-Lieb inequalities: Finiteness, structure and extremals
Bennett, Jonathan
Carbery, Anthony
Christ, Michael
Tao, Terence
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2007, 17 (05) : 1343 - 1415
[5] On the multilinear restriction and Kakeya conjectures
Bennett, Jonathan
Carbery, Anthony
Tao, Terence
[J]. ACTA MATHEMATICA, 2006, 196 (02) : 261 - 302
[6] Closure Properties of Solutions to Heat Inequalities
Bennett, Jonathan
Bez, Neal
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2009, 19 (03) : 584 - 600
[7] A sharp analog of Young's inequality on SN and related entropy inequalities
Carlen, EA
Lieb, EH
Loss, M
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2004, 14 (03) : 487 - 520
[8] Carlen EA, 2008, DOC MATH, V13, P553
[9] Foschi D, 2007, J EUR MATH SOC, V9, P739
[10] On sharp strichartz inequalities in low dimensions
Hundertmark, Dirk
Zharnitsky, Vadim
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2006, 2006

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