Vol. 4, No. 3, 2011

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Regularity of weak solutions of a complex Monge–Ampère equation

Gábor Székelyhidi and Valentino Tosatti

Vol. 4 (2011), No. 3, 369–378
Abstract

We prove the smoothness of weak solutions to an elliptic complex Monge–Ampère equation, using the smoothing property of the corresponding parabolic flow.

Keywords
complex Monge–Ampère equations, regularity of weak solutions, parabolic flows
Mathematical Subject Classification 2000
Primary: 32Q20, 32W20, 35J60
Secondary: 53C44
Milestones
Received: 11 December 2009
Accepted: 13 July 2010
Published: 28 December 2011
Authors
Gábor Székelyhidi
Department of Mathematics
University of Notre Dame
Notre Dame, IN 46556
United States
http://www.nd.edu/~gszekely
Valentino Tosatti
Department of Mathematics
Columbia University
2990 Broadway
New York, NY 10027
United States
http://www.math.columbia.edu/~tosatti