Perturbation of zero surfaces - Ramm, Alexander G. (Global Journal of Mathematical Analysis, 2017)
It is proved that if a smooth function \(u(x), x\in R^3\), 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 \(u(x)+ε v(x)\) has also a closed smooth surface \(S_ε\) of zeros. Here \(v\) is a smooth function and \(ε>0\) is a sufficiently small number.