Rigidity and flatness of the image of certain classes of mappings having tangential Laplacian

Hussien Abugirda, Birzhan Ayanbayev, Nikos Katzourakis

In this paper we consider the PDE system of vanishing normal projection of the Laplacian for $C^2$ maps $u:{\mathbb{R}}^n\supseteq \Omega ⟶{\mathbb{R}}^N$: \[ [\![\mathrm{D…