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arXiv · 1611.09602

Perturbation of zero surfaces

A. G. Ramm
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Abstract

It is proved that if a smooth function $u(x)$, $x\in \mathbb{R}^3$, such that $\inf_{s\in S}|u_N(s)|>0$, where $u_N$ is the normal derivative of $u$ on $S$, has a closed smooth surface $S$ of zeros, then the function $u(x)+\epsilon v(x)$ has also a closed smooth surface $S_\epsilon$ of zeros. Here $v$ is a smooth function and $\epsilon>0$ is a sufficiently small number.

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A. G. Ramm. 2016-11-29. Perturbation of zero surfaces. https://arxiv.org/abs/1611.09602

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