7 problems

Gurtin's conjecture. In the limit as $\varepsilon\to0$, any family of minimizers of $\{F_\varepsilon\}_{\varepsilon>0}$ should converge to a piecewise constant function that partit…

Second-order Gamma-limit conjecture. If $g$ has this form, then the limiting functional, with the same scaling $\varepsilon$, is proportional to the size of the jump set $J_g$.

Let $\Omega\subset\mathbb R^n$ be a bounded domain, let $u:\Omega\to\mathbb R$ denote the relative concentration of two phases with pure-phase values $u^-<u^+$, and consider the Ca…

The paper proposes a unified quasi-incompressible Navier–Stokes–Cahn–Hilliard model with non-matching densities. Direct-applicability conjecture. The approaches and techniques of A…

Saddle-point volume-constrained minimum conjecture. The saddle point is a volume-constrained minimum with “volume” approximately $\nu_s$.

Let $q\in(0,1)$ and suppose that the potential $W$ is symmetric about $(b+a)/2$. Let $\mathcal{F}_\varepsilon^{(1)}$ be the first-order functional and let $\min\mathcal{F}^{(1)}$ d…

Let $W$ be a potential with subquadratic growth near its wells, meaning that $q<1$ in the relevant hypothesis, and let the quantities and functionals in the first-order and second-…