A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

Title:

A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

Creator:

Schuhmache, Katrin

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0398929f-35df-47cc-b389-f550d5091218
uuid:0398929f-35df-47cc-b389-f550d5091218

Subject:

chart, coordinate transformation, normal vector, normal derivative, extension theorem, and Muckenhoupt weight

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Given a domain $\Omega $ of class $C^{k,1}$, $k\in \Bbb N $, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of $\Omega $ in the sense that $(\partial- {\partial x_n})\alpha (x',0)= - N(x')$ and that still is of class $C^{k,1}$. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to $k$ on domains of class $C^{k,1}$. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

637-648

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:3

Harvested from:

CDK

Metadata only:

false