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The Lin-Ni's Problem for Mean Convex Domains (Memoirs of the AMS) (Memoirs of the American Mathematical Society)

Mathematical Analysis

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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.

Product Specifications

Format: paperback
ASIN: 0821869094
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis
Domain: Amazon UK
Release Date: 15 June 2012
Listed Since: 27 April 2012

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The Lin-Ni's Problem for Mean Convex Domains (Memoirs of the AMS) (Memoirs of the American Mathematical Society)

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