Singularities of solutions of the Hamilton-Jacobi equation. A toy model: distance to a closed subset.
speaker: Albert Fathi (Georgia Institute of Technology)abstract:
This is a joint work with Piermarco Cannarsa and Wei Cheng.
If H : T∗ M → R is a Tonelli Hamiltonian, i.e. at least C2
convex and superlinear in the momentum, for a large class of viscosity solutions F : M × [0, +∞[→ R of the Hamilton-Jacobi equation
∂t F + H(x, ∂x F) = 0,
we describe the local structure of the set Sing(F) of points where F is not differentiable.
For example it is locally path-connected, and we will also study the homotopy type of
Sing(F).
We will give applications in Riemannian geometry.
These studies do cover the case of singularities of the Euclidean distance function
dA : Rk → [0, +∞[ to a closed subset A of the Euclidean space Rk. After considering the
results in the general case, we will concentrate on the case of dA to explain the methods
of proof.
timetable:
Wed 16 Jan, 9:30 - 10:30, Aula Magna Bruno Pontecorvo
documents:
Abstract
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