Analysis and PDE

Next Analysis and PDE seminar

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  • April, 27, 2023: Didier Pilod and Kundan Kumar, Bergen
    • Title: On some of Luis Caffarelli's comtributions
    • Abstract: In this seminar, we will discuss two of the many contributions of Caffarelli who was recently awarded the Abel prize.In the first part of talk, Didier will present the Caffarelli-Silvestre extension formula introduced in a seminal paper published in Comm. PDE in 2007. This formula characterizes the fractional Laplacian through an extension problem to the upper-half plane by solving a (degenerate) elliptic PDE. The interest of this formula lies in the fact that one can study properties of the fractional Laplacian, which is a non-local operator, by using local techniques on the extension problem.In the second part pf the talk, Kundan will discuss the contribution(s) of Caffarelli on free boundary and/or fully nonlinear equations.