The existence of k-convex hypersurface with prescribed mean curvature

Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2011-09, Vol.42 (1-2), p.43-72
Main Authors: Han, Fei, Ma, Xi-Nan, Wu, Damin
Format: Article
Language:English
Subjects:
Analysis
Calculus
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Curvature
Existence theorems
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Maximum principle
Partial differential equations
Systems Theory
Theorems
Theoretical
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Description
Summary:Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-010-0379-2