9 problems

Global mountain-pass minimizer conjecture. The global mountain pass solution is also a global constrained minimizer of the strain energy.

Boundary-attachment and curvature-selection conjecture. Attaching to the boundary remains optimal in convex domains $C^2$-close to a disk. In domains with non-constant boundary cur…

Boundary-attachment and monotonicity conjecture. Any minimiser in this regime touches the boundary of the unit disk, and the energy is increasing as the length $L$ increases.

Consider a circular cylindrical shell with a shape imperfection, such as a small localized dent, and let the trivial branch denote the unbuckled solution branch. Let the fundamenta…

Let $K(V_h)$ denote the Korn constant associated with the admissible space $V_h$, and consider buckling loads for axially compressed circular cylindrical shells. Imperfection-insen…

Shape-imperfection conjecture. An imperfection of shape can be mathematically described by such a tensor $\boldsymbol{\tau}^{0}$. This conjecture proposes a mathematical descriptio…

Load-imperfection conjecture. Imperfections of load can produce a non-homogeneous trivial branch leading to this form of $\boldsymbol{\tau}^{0}$ and hence to a dramatic change in t…

A circular cylindrical shell under uniform axial compression has three asymptotic buckling loads, of which the largest is realized in the perfect shell; the other two are significa…

Let $n\geq 2$ be an integer, and denote by $\sigma_{bn}$ and $\sigma_{cn}$ the buckling and contact pressures for the corresponding $n$-mode ring shape. For pressures satisfying…