In this paper, we prove the following general result: Let $X$ be a real Hilbert space and $J:X\to {\bf R}$ a $C1$ functional, with locally Lipschitzian derivative. Then, for each $x_0\in X$ with $J'(x_0)\neq 0$, there exists $\delta>0$ such that, for every $r\in ]0,\delta[$, the restriction of $J$ to the sphere $\{x\in X : \|x-x_0\|=r\}$ has a unique global minimum toward which every minimizing sequence strongly converges.

The problem of minimizing locally a C^2 functional around non-critical points is well-posed

RICCERI, Biagio
2007-01-01

Abstract

In this paper, we prove the following general result: Let $X$ be a real Hilbert space and $J:X\to {\bf R}$ a $C1$ functional, with locally Lipschitzian derivative. Then, for each $x_0\in X$ with $J'(x_0)\neq 0$, there exists $\delta>0$ such that, for every $r\in ]0,\delta[$, the restriction of $J$ to the sphere $\{x\in X : \|x-x_0\|=r\}$ has a unique global minimum toward which every minimizing sequence strongly converges.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/24505
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