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arXiv · 0805.3661

Boundary singularities of solutions of N-harmonic equations with absorption

Rouba Borghol·Laurent Veron
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Abstract

We study the boundary behaviour of solutions $u$ of $-Δ_{N}u+ |u|^{q-1}u=0$ in a bounded smooth domain $Ω\subset\mathbb R^{N}$ subject to the boundary condition $u=0$ except at one point, in the range $q>N-1$. We prove that if $q\geq 2N-1$ such a $u$ is identically zero, while, if $N-1<q<2N-1$, $u$ inherits a boundary behaviour which either corresponds to a weak singularity, or to a strong singularity. Such singularities are effectively constructed.

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Rouba Borghol, Laurent Veron. 2008-05-23. Boundary singularities of solutions of N-harmonic equations with absorption. https://arxiv.org/abs/0805.3661

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