2 problems

Consider the Helfrich Dirichlet problem for surfaces of revolution with boundary parameter $\alpha>0$ and weight parameter $\varepsilon\geq0$. Let $\alpha_m$ denote the threshold a…

Let $\alpha>0$ be fixed, let $\varepsilon_\alpha=\frac{1}{4\alpha^2}$, and let $(u_\varepsilon)_{\varepsilon\approx\varepsilon_\alpha}$ be the smooth local family of solutions to t…