Schauder theory for elliptic and parabolic PDEs

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Next lectures
12.10.2026, 11:00 (E2 10 (Leon-Lichtenstein))
19.10.2026, 11:00 (G3 10 (Lecture hall))
26.10.2026, 11:00 (E2 10 (Leon-Lichtenstein))
02.11.2026, 11:00 (E2 10 (Leon-Lichtenstein))
09.11.2026, 11:00 (E2 10 (Leon-Lichtenstein))
16.11.2026, 11:00 (E2 10 (Leon-Lichtenstein))
23.11.2026, 11:00 (E2 10 (Leon-Lichtenstein))
30.11.2026, 11:00 (E2 10 (Leon-Lichtenstein))
07.12.2026, 11:00 (E2 10 (Leon-Lichtenstein))
14.12.2026, 11:00 (E2 10 (Leon-Lichtenstein))
21.12.2026, 11:00 (E2 10 (Leon-Lichtenstein))
28.12.2026, 11:00 (E2 10 (Leon-Lichtenstein))
04.01.2027, 11:00 (E2 10 (Leon-Lichtenstein))
11.01.2027, 11:00 (E2 10 (Leon-Lichtenstein))
18.01.2027, 11:00 (E2 10 (Leon-Lichtenstein))
25.01.2027, 11:00 (E2 10 (Leon-Lichtenstein))

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The Schauder theory for linear parabolic and elliptic PDEs is an important result for many application, as for instance in the analysis of nonlinear equations. Following the method of Krylov-Safonov we study the Hölder regularity for linear elliptic and parabolic PDEs. In the first part of the course we will consider the Schuader theory for elliptic PDEs in Hölder spaces, for which several norms will be proved to be equivalent. In the second part of the course we will adapt Krylov-Safonov method to parabolic PDEs. If time allows, we will finally give the intuition of how the Schauder theory can be achieved also with energy methods in Campanato spaces.

Keywords
Schauder Theory, elliptic and parabolic PDE, Krylov-Safonov method, Hölder Spaces

Prerequisites
Basic Functional Analysis