Fulltext

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

Blatt, Simon ; Struwe, Michael

In: International Mathematics Research Notices, 2015, vol. 2015, no. 9, p. 2342-2385

Add to personal list
    Title
    • An Analytic Framework for the Supercritical Lane-Emden Equation and its Gradient Flow
    Author
    • Blatt, Simon. Fakultät für Mathematik, Karlsruher Institut für Technologie, D-76128 Karlsruhe, Germany
    • Struwe, Michael. Departement Mathematik, ETH-Zürich, CH-8092 Zürich, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • International Mathematics Research Notices, 2015, vol. 2015, no. 9, p. 2342-2385. Oxford University Press
    Other Version
    Classification
    • Health
    OAI-PMH Identifier
    • oai:doc.rero.ch:289234
    Summary
    The natural setting for the Lane-Emden equation −Δu=|u|p−2u on a domain $\Omega \subset \mathbb {R}^n$, n≥3, for supercritical exponents p>2*=2n/(n−2) is identified as the space of functions $u\in H^1_0\cap L^p(\Omega)$ 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