English

Singular limits for the bi-laplacian operator with exponential nonlinearity in $\R^4$

Analysis of PDEs 2015-05-13 v1

Abstract

Let Ω\Omega be a bounded smooth domain in R4\mathbb{R}^{4} such that for some integer d1d\geq1 its dd-th singular cohomology group with coefficients in some field is not zero, then problem {\Delta^{2}u-\rho^{4}k(x)e^{u}=0 & \hbox{in}\Omega, u=\Delta u=0 & \hbox{on}\partial\Omega, has a solution blowing-up, as ρ0\rho\to0, at mm points of Ω\Omega, for any given number mm.

Keywords

Cite

@article{arxiv.0709.2878,
  title  = {Singular limits for the bi-laplacian operator with exponential nonlinearity in $\R^4$},
  author = {Mónica Clapp and Claudio Muñoz and Monica Musso},
  journal= {arXiv preprint arXiv:0709.2878},
  year   = {2015}
}

Comments

30 pages, to appear in Ann. IHP Non Linear Analysis

R2 v1 2026-06-21T09:18:48.426Z