Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry
Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry
Abstract If $U:[0,+\infty [\times M$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>U</mml:mi> <mml:mo>:</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mo>+</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>[</mml:mo> <mml:mo>×</mml:mo> <mml:mi>M</mml:mi> </mml:math> is a uniformly continuous viscosity solution of the evolution Hamilton-Jacobi equation $$ \partial _{t}U+ H(x,\partial _{x}U)=0, $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>∂</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mi>U</mml:mi> <mml:mo>+</mml:mo> <mml:mi>H</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>∂</mml:mi> <mml:mi>x</mml:mi> …