On the spectrum of the double-layer operator on locally-dilation-invariant Lipschitz domains
On the spectrum of the double-layer operator on locally-dilation-invariant Lipschitz domains
Abstract We say that $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> , the boundary of a bounded Lipschitz domain, is locally dilation invariant if, at each $$x\in \Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Γ</mml:mi> </mml:mrow> </mml:math> , $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> is either locally $$C^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> …