We consider the problem of describing the traces of functions in \(H^2(\Omega )\) on the boundary of a Lipschitz domain \(\Omega \) of \(\mathbb R^N\), \(N\ge 2\). We provide a definition of those spaces, in particular of \(H^{\frac{3}{2}}(\partial \Omega )\), by means of Fourier series associated with the eigenfunctions of new multi-parameter biharmonic Steklov problems which we introduce with this specific purpose. These definitions coincide with the classical ones when the domain is smooth. Our spaces allow to represent in series the solutions to the biharmonic Dirichlet problem. Moreover, a few spectral properties of the multi-parameter biharmonic Steklov problems are considered, as well as explicit examples. Our approach is similar to that developed by G. Auchmuty for the space \(H^1(\Omega )\), based on the classical second order Steklov problem.

我们认为描述的功能的痕迹的问题\（H ^ 2（\欧米茄）\）一个李普希茨域的边界上\（\欧米茄\）的\（\ mathbb R 1Ñ\） ，\（N \ ge 2 \）。我们提供了这些空间的定义，尤其是\（H ^ {\ frac {3} {2}}（\ partial \ Omega} \）通过与新的多参数双调和Steklov问题的本征函数相关的傅里​​叶级数，我们为此专门介绍了这些问题。当域平滑时，这些定义与经典定义一致。我们的空间允许串联表示双调和Dirichlet问题的解决方案。此外，还考虑了多参数双谐波Steklov问题的一些频谱特性以及明确的示例。我们的方法类似于G. Auchmuty基于经典二阶Steklov问题针对空间\（H ^ 1（\ Omega）\）开发的方法。