Albert Fathi (Georgia Institute of Technology, USA) Viscosity solutions of the Hamilton-Jacobi equations on non-compact manifolds (10 hours) Schedule:
- Lecture 1: Tuesday June
1, 11-13 (UTC+2)
- Lecture 2: Friday June 4, 11-13 (UTC+2) - Lecture 3: Tuesday June 15, 11-13 (UTC+2) - Lecture 4: Thursday June 17, 11-13 (UTC+2) - Lecture 5: Tuesday June 22, 11-13 (UTC+2) Lectures will be streamed by the
platform Microsoft Teams.
- To subscribe to the Team of
the course (It is not necessary to
register to the Team in order to attend the streaming
of the lectures, see next item):
The identifying code of the Team
is tltqtrm
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link:
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attend the streaming of the lectures (it
works also for people that are not-member of the Team
and also without downloading the app, but directly via
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For any information,
contact Alfonso Sorrentino (sorrentin@mat.uniroma2.it)
Abstract The purpose of this
course is to study the properties of
viscosity solutions of the
Hamilton-Jacobi equations on non-compact
manifolds, in the spirit of what was done
for
the case of compact manifolds in We will be mainly interested in viscosity solutions of the evolution Hamilton-Jacobi equation ∂t U + H (x, ∂x U ) = 0. Here we think of
the case where U : [0, +∞[×M → R, with M is a manifold. When M is not compact, the global maximum principle does not immediately hold. We will show how to obtain the Lax-Oleinik formula and the uniqueness result. We will consider the pointwise finiteness of the Lax-Oleinik formula for general initial conditions. results. We will also
discuss results on
the topology of the set of singularities of
such solutions and give applications to
Riemannian
Geometry.
Note: This
series of lectures is part of the activity of
the MIUR Excellence Department Project
MATH@TOV CUP E83C18000100006
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