| D. COUTAND.[J].数学年刊A辑,1999,20(3):279~296 |
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| EXISTENCE OF MINIMIZING SOLUTIONS AROUND ``EXTENDED STATES''FOR A NONLINEARLY ELASTIC CLAMPED PLANE MEMBRANE |
| Received:October 22, 1998 Revised:February 09, 1999 |
| DOI： |
| 中文关键词: |
| 英文关键词:Minimizing solution, Nonlinearly elastic clamped plane membrane |
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| 中文摘要: |
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| 英文摘要: |
| The formal asymptotic analysis of D. Fox, A. Raoult
$\&$ J.C. Simo$^{[10]}$ has justified the two-dimensional
nonlinear ``membrane'' equations for a plate made of a Saint
Venant-Kirchhoff material.
This model, which retains the material-frame indifference of the
original three dimensional problem in the sense that its energy density is
invariant under the rotations of $\R^3$, is equivalent to finding the
critical points of a functional whose nonlinear part depends on the first
fundamental form of the unknown deformed surface.
The author establishes here, by the inverse function theorem, the existence
of an injective solution to the clamped membrane problem around particular
forces corresponding physically to an ``extension'' of the membrane.
Furthermore, it is proved that the solution found in this fashion is also the
unique minimizer to the nonlinear membrane functional, which is not
sequentially weakly lower semi-continuous. |
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