Inhomogeneous Strichartz estimates for Schrödinger's equation

Youngwoo Koh; Ihyeok Seo

doi:10.1016/j.jmaa.2016.04.061

Inhomogeneous Strichartz estimates for Schrödinger's equation

Youngwoo Koh
, Ihyeok Seo

Department of Mathematics

Korea Institute for Advanced Study

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Foschi and Vilela in their independent works [3,13] showed that the range of (1/r,1/r~) for which the inhomogeneous Strichartz estimate (norm of matrix)∫₀^te^i(t-s)δF(.,s)ds(norm of matrix)L_t^qL_x^r≲(norm of matrix)F(norm of matrix)L_t^q~'L_x^r~' holds for some q, q~ is contained in the closed pentagon with vertices A, B, B^', P, P^' except for the points P, P^' (see Fig. 1). We obtain the estimate for the corner points P, P^'.

Original language	English
Pages (from-to)	715-725
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	442
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.04.061
State	Published - 15 Oct 2016

Keywords

Schrödinger equation
Strichartz estimates

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10.1016/j.jmaa.2016.04.061

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title = "Inhomogeneous Strichartz estimates for Schr{\"o}dinger's equation",

abstract = "Foschi and Vilela in their independent works [3,13] showed that the range of (1/r,1/r\textasciitilde{}) for which the inhomogeneous Strichartz estimate (norm of matrix)∫0tei(t-s)δF(.,s)ds(norm of matrix)LtqLxr≲(norm of matrix)F(norm of matrix)Ltq\textasciitilde{}'Lxr\textasciitilde{}' holds for some q, q\textasciitilde{} is contained in the closed pentagon with vertices A, B, B', P, P' except for the points P, P' (see Fig. 1). We obtain the estimate for the corner points P, P'.",

keywords = "Schr{\"o}dinger equation, Strichartz estimates",

author = "Youngwoo Koh and Ihyeok Seo",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

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day = "15",

doi = "10.1016/j.jmaa.2016.04.061",

language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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T1 - Inhomogeneous Strichartz estimates for Schrödinger's equation

AU - Koh, Youngwoo

AU - Seo, Ihyeok

PY - 2016/10/15

Y1 - 2016/10/15

N2 - Foschi and Vilela in their independent works [3,13] showed that the range of (1/r,1/r~) for which the inhomogeneous Strichartz estimate (norm of matrix)∫0tei(t-s)δF(.,s)ds(norm of matrix)LtqLxr≲(norm of matrix)F(norm of matrix)Ltq~'Lxr~' holds for some q, q~ is contained in the closed pentagon with vertices A, B, B', P, P' except for the points P, P' (see Fig. 1). We obtain the estimate for the corner points P, P'.

AB - Foschi and Vilela in their independent works [3,13] showed that the range of (1/r,1/r~) for which the inhomogeneous Strichartz estimate (norm of matrix)∫0tei(t-s)δF(.,s)ds(norm of matrix)LtqLxr≲(norm of matrix)F(norm of matrix)Ltq~'Lxr~' holds for some q, q~ is contained in the closed pentagon with vertices A, B, B', P, P' except for the points P, P' (see Fig. 1). We obtain the estimate for the corner points P, P'.

KW - Schrödinger equation

KW - Strichartz estimates

UR - https://www.scopus.com/pages/publications/84966692231

U2 - 10.1016/j.jmaa.2016.04.061

DO - 10.1016/j.jmaa.2016.04.061

M3 - Article

AN - SCOPUS:84966692231

SN - 0022-247X

VL - 442

SP - 715

EP - 725

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Inhomogeneous Strichartz estimates for Schrödinger's equation

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