Localized energy for wave equations with degenerate trapping

Understand

Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry.

• Trapped rays necessitate a loss when compared to the estimate on Minkowski space.
• A loss of regularity is a common way to incorporate such.
• When trapping is sufficiently weak, a logarithmic loss of regularity suffices.