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The Dirichlet problem for the Lagrangian mean curvature equation

Arunima Bhattacharya

Vol. 17 (2024), No. 8, 2719–2736
Abstract

We solve the Dirichlet problem with continuous boundary data for the Lagrangian mean curvature equation on a uniformly convex, bounded domain in n.

Keywords
Lagrangian mean curvature, Dirichlet problem, comparison principles
Mathematical Subject Classification
Primary: 35J60
Milestones
Received: 26 February 2022
Revised: 7 February 2023
Accepted: 27 April 2023
Published: 12 October 2024
Authors
Arunima Bhattacharya
Department of Mathematics
University of North Carolina at Chapel Hill
Chapel Hill, NC
United States

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