Regularity of weak solutions of a complex Monge–Ampère equation

Székelyhidi, Gábor; Tosatti, Valentino

doi:10.2140/apde.2011.4.369

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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

DOI: 10.2140/apde.2011.4.369

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

Vol. 4, No. 3, 2011