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arXiv · 0904.3290

Asymptotics and quantization for a mean-field equation of higher order

Luca Martinazzi·Mircea Petrache
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Abstract

Given a regular bounded domain $Ω\subset\R{2m}$, we describe the limiting behavior of sequences of solutions to the mean field equation of order $2m$, $m\geq 1$, $$(-Δ)^m u=ρ\frac{e^{2mu}}{\int_Ωe^{2mu}dx}\quad\text{in}Ω,$$ under the Dirichlet boundary condition and the bound $0<ρ\leq C$. We emphasize the connection with the problem of prescribing the $Q$-curvature.

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Luca Martinazzi, Mircea Petrache. 2009-04-21. Asymptotics and quantization for a mean-field equation of higher order. https://doi.org/10.1080/03605300903296330

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