A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces |
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Authors: | Katrin Schumacher |
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Institution: | (1) Im kleinen Grund 30, 65779 Kelkheim, Germany;(2) Department of Mathematics, Darmstadt University of Technology, Schlossgartenstr. 7, 64289 Darmstadt, Germany |
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Abstract: | Given a domain Ω of class C
k,1, k ∈ ℕ, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of in the sense
that (∂/∂x
n
)α(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. |
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Keywords: | |
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