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The Lin-ni's Problem For Mean Convex Domains (memoirs Of The American Mathematical Society) by Olivier Druet, Frederic Robert, Druet, Juncheng Wei, Olivier/ Robert, Frederic/ Wei, Juncheng is a nonfiction available to read on EtoBox.

What is The Lin-ni's Problem For Mean Convex Domains (memoirs Of The American Mathematical Society) about?

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

Who reads The Lin-ni's Problem For Mean Convex Domains (memoirs Of The American Mathematical Society)?

Author

Olivier Druet, Frederic Robert, Druet, Juncheng Wei, Olivier/ Robert, Frederic/ Wei, Juncheng

Publisher

American Mathematical Society

Published

2012

Language

EN

ISBN

9780821890165

Category

nonfiction

Subjects

Mathematics, Stem