Use cases of Holder continuity in Machine Learning domain part8

1. A note on the Trace Theorem for domains which are locally subgraph of a Holder continuous function(arXiv)

Author : Boris Muha

Abstract : The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a H\” older continuous function. More precisely, let η∈C0,α(ω), 0<α<1 and let Ωη be a domain which is locally subgraph of a function η. We prove that mapping γη:u↦u(x,η(x)) can be extended by continuity to a linear, continuous mapping from H1(Ωη) to Hs(ω), s<α/2. This study is motivated by analysis of fluid-structure interaction problems.

2. Holder continuity for the ring Q-homeomorphisms with respect to p-modulus(arXiv)

Author : Ruslan Salimov

Abstract : It is founded the sufficient condition of Holder continuity of the ring Q-homeomorphisms in Rn,n≥2 with respect to p-modulus at n−1<p<n.