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arXiv · 1811.12849

Functional characterizations of trace spaces in Lipschitz domains

Soumia Touhami·Abdellatif Chaira·Delfim F. M. Torres
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Abstract

Using a factorization theorem of Douglas, we prove functional characterizations of trace spaces $H^s(\partial \Omega)$ involving a family of positive self-adjoint operators. Our method is based on the use of a suitable operator by taking the trace on the boundary $\partial \Omega$ of a bounded Lipschitz domain $\Omega \subset \mathbb R^d$ and applying Moore--Penrose pseudo-inverse properties together with a special inner product on $H^1(\Omega)$. Moreover, generalized results of the Moore--Penrose pseudo-inverse are also established.

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Soumia Touhami, Abdellatif Chaira, Delfim F. M. Torres. 2018-11-30. Functional characterizations of trace spaces in Lipschitz domains. https://doi.org/10.1215/17358787-2018-0044

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