A necessary condition in a De Giorgi type conjecture for elliptic systems in infinite strips
Radu Ignat, Antonin Monteil · arXiv (Cornell University) · 2019
Given a bounded Lipschitz domain $ω\subset\mathbb{R}^{d-1}$ and a lower semicontinuous function $W:\mathbb{R}^N\to\mathbb{R}_+\cup\{+\infty\}$ that vanishes on a finite set and that is bounded from below by a positive constant at infinity, we show that every map $u:\mathbb{R}\timesω\to\mathbb{R}^N$ with \[ \int_{\mathbb{R}\timesω}\big(\lvert abla u\rvert^2+W(u)\big)\mathop{}\mathopen{}\mathrm{d} x_1\mathop{}\mathopen{}\mathrm{d}x'