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Item Details
| Title:
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THE LIN-NI'S PROBLEM FOR MEAN CONVEX DOMAINS
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| By: |
Olivier Druet, Frederic Robert, Juncheng Wei |
| Format: |
Paperback |
| List price:
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£66.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821869094 |
| ISBN 13: |
9780821869093 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 June, 2012 |
| Series: |
Memoirs of the American Mathematical Society 218, 1027 |
| Pages: |
105 |
| Description: |
"July 2012, volume 218, number 1027 (end of volume)." |
| Synopsis: |
The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition. |
| Illustrations: |
Illustrations |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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