The Lin-Ni's Problem for Mean Convex Domains

Olivier Druet, Frederic Robert, Juncheng Wei (Autoren)

Buch | Softcover

105 Seiten

2012
American Mathematical Society (Verlag)
978-0-8218-6909-3 (ISBN)

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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.

Erscheint lt. Verlag	1.7.2012
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Gewicht	180 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-6909-4 / 0821869094
ISBN-13	978-0-8218-6909-3 / 9780821869093
Zustand	Neuware