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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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Published in: | Calculus of variations and partial differential equations 2011-09, Vol.42 (1-2), p.43-72 |
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cites | cdi_FETCH-LOGICAL-c347t-e9497ed1de85fcd4b8e27e773703b0bf8065789ac5e12e1c50c4e8acfb363d0d3 |
container_end_page | 72 |
container_issue | 1-2 |
container_start_page | 43 |
container_title | Calculus of variations and partial differential equations |
container_volume | 42 |
creator | Han, Fei Ma, Xi-Nan Wu, Damin |
description | 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
. |
doi_str_mv | 10.1007/s00526-010-0379-2 |
format | article |
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k
-convex starshaped hypersurface with prescribed mean curvature in
R
n
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k
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k
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R
n
+1
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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 |
title | The existence of k-convex hypersurface with prescribed mean curvature |
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