English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the problem of describing the traces of functions in$H^2(\Omega)$ on the boundary of a Lipschitz domain $\Omega$ of $\mathbb R^N$,$N\geq 2$. We provide a definition of those spaces, in particular of$H^{\frac{3}{2}}(\partial\Omega)$, by means of Fourier series associated withthe eigenfunctions of new multi-parameter biharmonic Steklov problems which weintroduce with this specific purpose. These definitions coincide with theclassical ones when the domain is smooth. Our spaces allow to represent inseries the solutions to the biharmonic Dirichlet problem. Moreover, a fewspectral properties of the multi-parameter biharmonic Steklov problems areconsidered, as well as explicit examples. Our approach is similar to thatdeveloped by G. Auchmuty for the space $H^1(\Omega)$, based on the classicalsecond order Steklov problem.

On the explicit representation of the trace space $H^{\frac{3}{2}}$ and  of the solutions to biharmonic Dirichlet problems on Lipschitz domains via  multi-parameter Steklov problems