A threshold phenomenon for embeddings of {H^m_0} into Orlicz spaces

Martinazzi, Luca. (2009) A threshold phenomenon for embeddings of {H^m_0} into Orlicz spaces. Calculus of Variations and Partial Differential Equations, 36 (4). pp. 493-506.

Full text not available from this repository.

Official URL: http://edoc.unibas.ch/49896/

Downloads: Statistics Overview


Given an open bounded domain {\Omega\subset\mathbb {R}^{2m}} with smooth boundary, we consider a sequence {(u_k)_{k\in\mathbb{N}}} of positive smooth solutions to
\left\{\begin{array}{ll} (-\Delta)^m u_k=\lambda_k u_k e^{mu_k^2} \quad\quad\quad\quad\quad {\rm in}\,\Omega\\ u_k=\partial_\nu u_k=\cdots =\partial_\nu^{m-1} u_k=0 \quad {\rm on }\, \partial \Omega, \end{array}\right.
where λk → 0+.
Assuming that the sequence is bounded in {H^m_0(\Omega)} , we study its blow-up behavior. We show that if the sequence is not precompact, then
\liminf_{k\to\infty}\|u_k\|^2_{H^m_0}:=\liminf_{k\to\infty}\int\limits_\Omega u_k(-\Delta)^m u_k dx\geq \Lambda_1,
where Λ1 = (2m − 1)!vol(S2m) is the total Q-curvature of S2m.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik
UniBasel Contributors:Martinazzi, Luca
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:09 Jan 2018 08:50
Deposited On:09 Jan 2018 08:50

Repository Staff Only: item control page