7 problems

Let $M_3(\lambda,c_0)$ be the cubic supremum, and let $c_1(\lambda)$ be a threshold such that $M_3(\lambda,c_0)=M_3(\lambda,c_1)$ for all $c_0\geq c_1(\lambda)$. For…

Let $G$ be the energy function and let $M_2(\lambda,c_0)$ denote the corresponding supremum, with parameters $\lambda>0$ and $c_0>0$. Quadratic-supremum conjecture. For all…

For $n\in\mathbb{N}$, let $\lambda_1,\lambda_2,\ldots,\lambda_n,\mu_1,\mu_2,\ldots,\mu_n\in\mathbb{R}_+$, and let … be the elementary symmetric polynomials. The sum of squared loga…

Let $U$ be the right stretch tensor and let $K_2^2=\|\operatorname{dev}_n\log U\|^2$. Global TSTS-M$^+$ nonexistence conjecture. For $n=2,3$, there is no elastic energy of the form…

Rank-one convexity region conjecture. For $n=2,3$, the energy $F\mapsto\frac{\mu}{k}e^{k\|\operatorname{dev}_n\log U\|^2}$ with $k>\frac{3}{16}$ is rank-one convex on a set contain…

For $F\in\mathbb{R}^{n\times n}$, define the exponentiated Hencky energy by … where $U$ is the right stretch tensor and $\mu,\kappa,k,\widehat{k}$ are parameters. Planar polyconvex…

Let $W_{\rm eH}$ denote the exponentiated Hencky-logarithmic strain energy, and let E$^+$-TSS denote the strict tension–tension stress inequalities. The exponentiated Hencky energy…