Abstract
For concentrating solutions \(0 < u_k \rightharpoonup 0\) weakly in H 2(Ω) to the equation \(\Delta^{2} u_{k}= \lambda_{k} u_{k} e^{2u_{k}^{2}}\) on a domain \(\Omega \subset \mathbb{R}^{4}\) with Navier boundary conditions the concentration energy \(\Lambda = \lim_{k \rightarrow \infty} \int_{\Omega} |\Delta u_k|^{2} dx\) is shown to be strictly quantized in multiples of the number \(\Lambda_1 = 16 \pi^{2}\).
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Struwe, M. Quantization for a fourth order equation with critical exponential growth. Math. Z. 256, 397–424 (2007). https://doi.org/10.1007/s00209-006-0081-4
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DOI: https://doi.org/10.1007/s00209-006-0081-4