Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robin eigenvalues on domains with peaks   Let $\Omega\subset\mathbb{R}^N$, $N\ge 2,$ be a bounded domain with an
outward power-like peak which is assumed not too sharp in a suitable sense. We
consider the Laplacian $u\mapsto -\Delta u$ in $\Omega$ with the Robin boundary
condition $\partial_n u=\alpha u$ on $\partial\Omega$ with $\partial_n$ being
the outward normal derivative and $\alpha>0$ being a parameter. We show that
for large $\alpha$ the associated eigenvalues $E_j(\alpha)$ behave as
$E_j(\alpha)\sim -\epsilon_j \alpha^\nu$, where $\nu>2$ and $\epsilon_j>0$
depend on the dimension and the peak geometry. This is in contrast with the
well-known estimate $E_j(\alpha)=O(\alpha^2)$ for the Lipschitz domains.

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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph