The Sobolev Wavefront Set of the Causal Propagator in Finite Regularity
The Sobolev Wavefront Set of the Causal Propagator in Finite Regularity
Abstract Given a globally hyperbolic spacetime $$M={\mathbb {R}}\times \Sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>×</mml:mo> <mml:mi>Σ</mml:mi> </mml:mrow> </mml:math> of dimension four and regularity $$C^\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mi>τ</mml:mi> </mml:msup> </mml:math> , we estimate the Sobolev wavefront set of the causal propagator $$K_G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>K</mml:mi> …