On the second boundary value problem for a class of fully nonlinear flow III

We study the solvability of the second boundary value problem of the Lagrangian mean curvature equation arising from special Lagrangian geometry. By the parabolic method, we obtain the existence and uniqueness of the smooth uniformly convex solution, which generalizes the Brendle–Warren’s theorem ab...

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Bibliographic Details
Published in:Journal of evolution equations 2024-09, Vol.24 (3), Article 52
Main Authors: Wang, Chong, Huang, Rongli, Bao, Jiguang
Format: Article
Language:English
Subjects:
Analysis
Boundary value problems
Euclidean geometry
Isomorphism
Mathematics
Mathematics and Statistics
Metric space
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Summary:We study the solvability of the second boundary value problem of the Lagrangian mean curvature equation arising from special Lagrangian geometry. By the parabolic method, we obtain the existence and uniqueness of the smooth uniformly convex solution, which generalizes the Brendle–Warren’s theorem about minimal Lagrangian diffeomorphism in Euclidean metric space.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-024-00983-6