7 problems

Let $p\in(1,\infty)$ and $t_{\max}>0$. For each natural number $n$, let $(\hat{k}_n,\hat{\mu}_n)\in L^\infty(\Omega;\mathbb{R}_+)^2$ solve the (vp-IMD) problem, respectively the (s…

Three-dimensional Gamma-limit conjecture. For $n=3$ and $\rho\to0$, if $\zeta\in(\zeta_0,\zeta_1)$, the Gamma-limit of $F'_\rho$ is a quadratic form in the principal curvatures for…

Let $n\geq 2$ be an integer, let $E\subset \mathbb{R}^n$ have boundary $\Sigma:=\partial E$ of class $C^2$, and let $\Omega\subset \mathbb{R}^n$ be open. For $\lambda>0$, define ……

Three-dimensional vectorial Gamma-limit conjecture. If $\boldsymbol u\in L^2(\mathcal{O};\mathbb{R}^3)$ and…

Formal compactness and lim-inf conjecture. There exists a subsequence, not relabelled, such that

Smooth density conjecture. Smooth functions are strongly dense in $\Xi^{\kappa_m,p}$. In particular,

Higher-order line-tension conjecture. Under the hypotheses of Theorem, the sequence $\{\mathcal{F}_{\varepsilon}\}_{\varepsilon>0}$ $\Gamma$-converges as $\varepsilon\to0^+$ to