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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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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 $p=1+4/n$. |
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| ISSN: | 1072-6691 |