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Seminar

OT Programmatic Seminar: Sub-level Set Convex Analysis October 22, 2013 (04:45 PM PDT - 05:45 PM PDT)
Parent Program: Optimal Transport: Geometry and Dynamics
Location: MSRI: Baker Board Room
Speaker(s) Robert Jensen (Loyola University)
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Upper semi-continuous functions which have sub-level convex sets are close cousins to and contain the convex functions.  Such functions are also called quasi-convex (e.g., http://en.wikipedia.org/wiki/Quasiconvex_function), but this term also can refer to functions which give rise to functionals that are weakly lower semi-continuous.  In this talk I will investigate the connection between sub-level set convex functions and a nonlinear, degenerate elliptic PDE.  I will describe properties of solutions of this PDE, including existence, uniqueness, and regularity.  The context for this work is in the Crandall-Lions theory of viscosity solutions.

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