A necessary condition in a De Giorgi type conjecture for elliptic systems in infinite strips
Year: 2019
Type: preprint
Abstract: 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\nabla u\rvert^2+W(u)\big)\mathop{}\mathopen{}\mathrm{d} x_1\mathop{}\mathopen{}\mathrm{d}x'
Source: arXiv (Cornell University)
Authors: Ignat, Radu, Monteil, Antonin
Institution: Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2944923529