# Quantization for an elliptic equation of order 2m with critical exponential non-linearity

Martinazzi, Luca and Struwe, Michael. (2012) Quantization for an elliptic equation of order 2m with critical exponential non-linearity. Mathematische Zeitschrift, 270 (1-2). pp. 453-487.

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On a smoothly bounded domain ${\Omega\subset\mathbb{R}^{2m}}$ we consider a sequence of positive solutions ${u_k\stackrel{w}{\rightharpoondown}0}$ in H m (Ω) to the equation ${(-\Delta)^m u_k=\lambda_k u_k e^{mu_k^2}}$ subject to Dirichlet boundary conditions, where 0 < λ k → 0. Assuming that
$$0 < \Lambda:=\lim_{k\to\infty}\int\limits_\Omega u_k(-\Delta)^m u_k dx < \infty,$$