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
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- 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