Calculus of Variations and Geometric Measure Theory

G. Fusco - G. F. Gronchi - M. Novaga

On the existence of connecting orbits for critical values of the energy

created by novaga on 26 Jan 2017
modified on 12 Oct 2017


Published Paper

Inserted: 26 jan 2017
Last Updated: 12 oct 2017

Journal: J. Differential Eqs.
Volume: 263
Number: 12
Pages: 8848-8872
Year: 2017


We consider an open connected set $\Omega$ and a smooth potential $U$ which is positive in $\Omega$ and vanishes on $\partial\Omega$. We study the existence of orbits of the mechanical system $\ddot{u}=U_x(u)$, that connect different components of $\partial\Omega$ and lie on the zero level of the energy. We allow that $\partial\Omega$ contains a finite number of critical points of $U$. The case of symmetric potential is also considered.