Seminar

Quasiconformal maps and the Monge-Ampère equation

Seminario periodico del Dipartimento di Matematica
21 May 2024
Start time 
2:00 pm
Polo Ferrari 1 - Via Sommarive 5, Povo (Trento)
Aula A220
Target audience: 
University community
UniTrento students
Attendance: 
Free
Contact person: 
Andrea Marchese, Andrea Pinamonti e Paolo Bonicatto
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 0461/281508-1625-1701-1980-1511
Speaker: 
André Guerra (ETH Zurigo)

Abstract

In the complex plane, there is a surprising correspondence between solutions of the Monge--Ampère equation and solutions of a certain differential inclusion associated to SO(2). Under this correspondence, the $W^{2,p}$ regularity of solutions to Monge--Ampère corresponds to a precise unique continuation principle for solutions of the differential inclusion. We will sketch a proof of the latter, which relies on quasiconformal maps and the rigidity estimate for SO(2). This proof also yields new results for nonlinear Beltrami equations in the plane. The talk is based on joint work with G. De Philippis and R. Tione.

Eventi passati

È possibile consultare gli eventi del precedente ciclo alla pagina dedicata