243240 IRTG Topics Lecture: Analysis of differential and integro-differential equations (V) (WiSe 2023/2024)

I will explain the method of De Giorgi for second-order PDE and, which is the main focus, for equations involving nonlocal operators of fractional order.

Requirements for participation, required level

Some knowledge of partial differential equations and function spaces

Bibliography

Han, Qing (1-NDM); Lin, Fanghua (1-NY-X)
Elliptic partial differential equations.
Second edition. Courant Lecture Notes in Mathematics, 1. Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2011. x+147 pp. ISBN: 978-0-8218-5313-9

MR1962933 (2004g:49003) Reviewed
Giusti, Enrico (I-FRNZ)
Direct methods in the calculus of variations. World Scientific Publishing Co., Inc., River Edge, NJ, 2003. viii+403 pp. ISBN: 981-238-043-4

Gilbarg, David (1-STF); Trudinger, Neil S. (5-ANUM)
Elliptic partial differential equations of second order.
Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001. xiv+517 pp. ISBN: 3-540-41160-7

Caffarelli, Luis A. (1-TX); Vasseur, Alexis F. (1-TX)
The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. (English summary)
Discrete Contin. Dyn. Syst. Ser. S 3 (2010), no. 3, 409–427.