Energy asymptotics in the Brezis–Nirenberg problem: The higher-dimensional case
For dimensions $N \geq 4$, we consider the Br\'ezis-Nirenberg variational problem of finding \[ S(\epsilon V) := \inf_{0\not\equiv u\in H^1_0(\Omega)} \frac{\int_\Omega |\nabla u|^2\, dx +\epsilon \int_\Omega V\, |u|^2\, dx}{\left(\int_\Omega |u|^q \, dx \right)^{2/q}}, \] where $q=\frac{2N}{N-...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-05-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2020007/fulltext.html |