Remarks on the sharp constant for the Schrodinger Strichartz estimate and applications
In this article, we compute the sharp constant for the homogeneous Schrodinger Strichartz inequality, and for the Fourier restriction inequality on the paraboloid in any dimension under the condition conjectured (and proved for dimensions 1 and 2) that the maximizers are Gaussians. We observ...
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Texas State University
2015-10-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/270/abstr.html |
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doaj-5f6bf997070745119858b8a6f32eed0d2020-11-25T01:03:25ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-10-012015270,119Remarks on the sharp constant for the Schrodinger Strichartz estimate and applicationsAlessandro Selvitella0 McMaster Univ., Hamilton, Ontario, Canada In this article, we compute the sharp constant for the homogeneous Schrodinger Strichartz inequality, and for the Fourier restriction inequality on the paraboloid in any dimension under the condition conjectured (and proved for dimensions 1 and 2) that the maximizers are Gaussians. We observe also how this would imply a far from optimal, but "cheap" and sufficient, criterion of the global wellposedness in the $L^2$-critical case $p=1+4/n$.http://ejde.math.txstate.edu/Volumes/2015/270/abstr.htmlStrichartz estimateoptimal constantSchrodinger equationrestriction inequality |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alessandro Selvitella |
| spellingShingle |
Alessandro Selvitella Remarks on the sharp constant for the Schrodinger Strichartz estimate and applications Electronic Journal of Differential Equations Strichartz estimate optimal constant Schrodinger equation restriction inequality |
| author_facet |
Alessandro Selvitella |
| author_sort |
Alessandro Selvitella |
| title |
Remarks on the sharp constant for the Schrodinger Strichartz estimate and applications |
| title_short |
Remarks on the sharp constant for the Schrodinger Strichartz estimate and applications |
| title_full |
Remarks on the sharp constant for the Schrodinger Strichartz estimate and applications |
| title_fullStr |
Remarks on the sharp constant for the Schrodinger Strichartz estimate and applications |
| title_full_unstemmed |
Remarks on the sharp constant for the Schrodinger Strichartz estimate and applications |
| title_sort |
remarks on the sharp constant for the schrodinger strichartz estimate and applications |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2015-10-01 |
| description |
In this article, we compute the sharp constant for the homogeneous
Schrodinger Strichartz inequality, and for the Fourier restriction
inequality on the paraboloid in any dimension under the condition
conjectured (and proved for dimensions 1 and 2) that the maximizers
are Gaussians. We observe also how this would imply a far from optimal,
but "cheap" and sufficient, criterion of the global wellposedness
in the $L^2$-critical case $p=1+4/n$. |
| topic |
Strichartz estimate optimal constant Schrodinger equation restriction inequality |
| url |
http://ejde.math.txstate.edu/Volumes/2015/270/abstr.html |
| work_keys_str_mv |
AT alessandroselvitella remarksonthesharpconstantfortheschrodingerstrichartzestimateandapplications |
| _version_ |
1725201401480478720 |