Minitutorial: Some Non Linear Problems Involving Integral Diffusions

Monday, December 7 and Tuesday, December 8
2:00 PM - 3:30 PM
Symphony I

Problems involving integral diffusion appear in questions of continuum mechanics ( in variational , or "divergence form" ) and in probability and optimal control, from Levi processes, in " non divergence" form. In the first case, to develop a non linear theory ( similar to quasilinear equations in the calculus of variations, it is necessary to develop the equivalent of the De Giorgi,Nash, Moser theory for " bounded measurable kernels coming from non local variational integrals in energy spaces of fractional derivatives. In the second, parallel to the theory of optimal control,the theory parallels the Krylov Safanov Harnack inequality and the Evans Krylov theorem. We will present the main ideas and arguments of the corresponding non local theorems.

Luis Caffarelli
University of Texas at Austin

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