What question did this study set out to answer?

This research aims to establish the regularity of certain renormalized value functions for the N-body problem by analyzing their solutions.

On the Regularity of Solutions to the Hamilton–Jacobi Equations for the N-Body Problem

View Full Paper

Ask AI

Bookmark

Authors

Theorem shows viscosity solutions exist for the N-body problem, implying insights on singularities.

This research aims to establish the regularity of certain renormalized value functions for the N-body problem by analyzing their solutions.
Proved that specific value functions are viscosity solutions of the Hamilton–Jacobi equation.
Analyzed singularities to define configurations with non-unique minimizers.
Estimated closure size of the singular set using the Hausdorff rectifiability.
Proved that the singular set has ^{d(N-1)-1} rectifiability.
Established an upper bound on the Hausdorff dimension of regular conjugate points.

Berti et al. (2026) studied this question.

View Full Paper

Ask AI

Bookmark