Mikolaj Sierzega (Cornell - University of Warsaw)
Title: Li-Yau-Type Bounds for the Fractional Heat Equation
Abstract: Differential Harnack bounds are a key analytical device that bridge partial differential equations of the elliptic or parabolic type with Harnack bounds, which provide pointwise estimates on the local variability of solutions. A prime example is the famous Li-Yau inequality, which applies to positive solutions of the classical heat equation. The growing interest in the theory and applications of nonlocal diffusion models naturally raises questions about analogues of Li-Yau-type inequalities in the nonlocal setting. However, despite many parallels between local and nonlocal diffusion models, even the model case of fractional heat flow presents both conceptual and technical challenges. In my talk, I will discuss recent progress on optimal differential Harnack bounds for fractional heat flow. In particular, I will show how the structural properties of these estimates offer new insights into classical results for the standard heat equation.
Where: Pavillion Andr茅-Aisenstadt, room 5183, and by Zoom (see link below)
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Meeting ID: 682 6260 1278
Passcode: 127830
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