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A Nonlinear Interpolation Theorem with Applications to Nonlinear Diffusion Problems April 17, 2017 Department NewsEventsSeminars

Dr. Daniel Hauer

University of Sydney

In this talk, I want to present a new nonlinear interpolation theorem, which improves Peetres (Theorem 3.1 in [Mathematica1970]) and Tartars (Théorème 4 in [JFA1972]) nonlinear interpolation results. In order to highlight the strength of this result, I will provide a new method to derive global Lq - L regularization estimates for 1 ≤ q < ∞ of solutions of nonlinear diffusion problems. On the one hand, this method simplifies the known ones for all solutions of the class of nonlinear diffusion problems where the principal operator has similar properties as the local p-Laplace operator (1 ≤ p < ∞ ). On the other hand, this method provides a very efficient and strong way to establish global L1 - L regularization estimates of solutions of the class of nonlocal diffusion problems driven by the fractional p-Laplace operator (1 ≤ p < ∞ ).

The results are obtained in joint work with Professor Thierry Coulhon (President of PSL Research University, Paris) and are part of the new book "Regularization effects of nonlinear semigroups - Theory and Applications" to appear under BCAM SPRINGERBRIEFS.

Tuesday, April 25

FLN 4.01.20

4:00 - 5:00 PM