Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains

Xavier Lamy, Petru Mironescu

Let $\Omega$ be a smooth bounded simply connected domain in ${\mathbb{R}}^2$. We investigate the existence of critical points of the energy $E_\varepsilon (u)=1/2\int_Ω|\nabla u|^2+1/(4\v…