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Quantization effects for a fourth order equation of exponential growth in dimension four | Frederic Robert
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7 Dec 2005 | Subject: | Analysis of PDEs | Abstract: | We investigate the asymptotic behavior as $k o +infty$ of sequences $(u_k)_{kinmathbb{N}}in C^4(Omega)$ of solutions of the equations $Delta^2 u_k=V_k e^{4u_k}$ on $Omega$, where $Omega$ is a bounded domain of $mathbb{R}^4$ and $lim_{k o +infty}V_k=1$ in $C^0_{loc}(Omega)$. The corresponding 2-dimensional problem was studied by Br’ezis-Merle and Li-Shafrir who pointed out that there is a quantization of the energy when blow-up occurs. As shown by Adimurthi, Struwe and the author, such a quantization does not hold in dimension four for the problem in its full generality. We prove here that under natural hypothesis on $Delta u_k$, we recover such a quantization as in dimension 2. | Source: | arXiv, math/0512148 | Services: | Forum | Review | PDF | Favorites |
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