This article is cited in 3 papers

The Boundary Behavior of Functions of Sobolev Spaces Defined on a Planar Domain with a Peak Vertex on the Boundary

M. Yu. Vasil'chik

Novosibirsk State Technical University

Abstract: Let $G$ be a domain with piecewise smooth boundary $\partial G$ and with vertices of exterior peaks on the boundary and let $k$ functions $f_1,\dots,f_k$ ($k$ is a nonnegative integer) be given on $\partial G$.
We find necessary and sufficient conditions for existence of a function $F\in W_p^l(G)$, where $1<p<\infty$ and $l\geqslant k+1$ is an integer, such that $\frac{\partial^r F}{\partial N^r} \bigr\vert_{\partial G}=f_r$, $r=0,1,\dots,k$, with $N$ a unit vector field defined on $\partial G$ and nontangent to $\partial G$.

Key words: Sobolev space, exterior peak, trace on the boundary, trace space.

UDC: 517.518.234

Received: 13.12.2001

 English version: Siberian Advances in Mathematics, 2004, 14:2, 92–115

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