Calculus of Variations and Geometric Measure Theory
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G. Bellettini - A. De Masi - E. Presutti

Energy levels of critical points of a nonlocal functional

created on 22 Sep 2004
modified by belletti on 23 Dec 2005


Accepted Paper

Inserted: 22 sep 2004
Last Updated: 23 dec 2005

Journal: J. Math. Phys.
Year: 2004


We study the critical points of a non local free energy functional, which has two ground states, $m^{(\pm)}$, with zero energy, and we prove that the first excited state is the instanton $\hat m_L$ introduced in \cite{DOP2}, \cite{BDR}, \cite{CR}. The result completes the analysis initiated in \cite{BeDePr:04a} on the ``tunnelling'' between $m^{(\pm)}$.

Keywords: Nonlocal functionals, critical points

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