Student Analysis Seminar

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Blow-up Methods for Schauder Estimates: From Elliptic to Kinetic Equations

Speaker: Grayson Davis, NYU Courant

Location: Warren Weaver Hall 201

Date: Monday, March 2, 2026, 12:30 p.m.

Synopsis:

We illustrate the blow-up method of Leon Simon (1997) for proving Schauder estimates for elliptic PDE. While Schauder estimates can be obtained through various other approaches, the blow-up method provides a robust framework that naturally extends to numerous problems in PDE and geometric analysis. We will apply this approach to prove a Schauder estimate for elliptic operators in non-divergence form. To further demonstrate the flexibility of the blow-up method, we will conclude by examining Schauder estimates for kinetic integral equations, as formulated by Imbert & Silvestre (2021), and discussing their applications to global regularity estimates for the Boltzmann equation without cut-off.