An Analytic Framework for the Supercritical Lane-Emden Equation and its Gradient Flow

被引：9

作者：

Blatt, Simon ^{[1
]}

Struwe, Michael ^{[2
]}

机构：

[1] Karlsruhe Inst Technol, Fak Math, D-76128 Karlsruhe, Germany

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2015年 / 2015卷 / 09期

基金：

瑞士国家科学基金会;

关键词：

PARTIAL REGULARITY; POSITIVE SOLUTIONS; BLOW-UP; ASYMPTOTIC-BEHAVIOR; ELLIPTIC-EQUATIONS; WEAK SOLUTIONS; HARMONIC MAPS; II BLOWUP; DOMAINS;

D O I：

10.1093/imrn/rnt359

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The natural setting for the Lane-Emden equation -Delta u = vertical bar u vertical bar(p-2)u on a domain Omega subset of R-n, n >= 3, for supercritical exponents p > 2* = 2n/(n-2) is identified as the space of functions u is an element of H-0(1) boolean AND L-p(Omega) with finite scale-invariant Morrey norms. We show that this Morrey regularity is propagated by the heat flow associated with this equation, and we study the blow-up profiles.

引用

页码：2342 / 2385

页数：44

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