Planar Sobolev extension domains and a Square Separation Theorem

Seminar
Speaker
Prof. P. Shvartsman, Technion
Date
19/01/2015 - 15:00 - 14:00Add to Calendar 2015-01-19 14:00:00 2015-01-19 15:00:00 Planar Sobolev extension domains and a Square Separation Theorem For each positive integer $m$ and each $p>2$ we characterize bounded simply connected Sobolev $W^m_p$-extension domains $\Omega$ in $R^2$. Our criterion is expressed in terms of certain intrinsic subhyperbolic metrics in $\Omega$. Its proof is based on a series of results related to the existence of special chains of squares joining given points $x$ and $y$ in $\Omega$. An important geometrical ingredient for obtaining these results is a new ''Square Separation Theorem''. It states that under certain natural assumptions on the relative positions of a point $x$ and a square $S\subset\Omega$ there exists a similar square $Q\subset\Omega$ which touches $S$ and has the property that $x$ and $S$ belong to distinct connected components of $\Omega\setminus Q$.  This is a joint work with Nahum Zobin. 2nd floor Colloquium Room, Building 216 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
2nd floor Colloquium Room, Building 216
Abstract

For each positive integer $m$ and each $p>2$ we characterize bounded simply connected
Sobolev $W^m_p$-extension domains $\Omega$ in $R^2$. Our criterion is expressed in terms of
certain intrinsic subhyperbolic metrics in $\Omega$. Its proof is based on a series of results related
to the existence of special chains of squares joining given points $x$ and $y$ in $\Omega$.

An important geometrical ingredient for obtaining these results is a new ''Square Separation Theorem''.
It states that under certain natural assumptions on the relative positions of a point $x$ and a square
$S\subset\Omega$ there exists a similar square $Q\subset\Omega$ which touches $S$ and has
the property that $x$ and $S$ belong to distinct connected components of $\Omega\setminus Q$.

 This is a joint work with Nahum Zobin.

תאריך עדכון אחרון : 12/01/2015