8 problems

Schaeffer's conjecture. Generically, the weak solution of the obstacle problem is also a strong solution, in the sense that the free boundary is a $C^\infty$ manifold. Equivalently…

Let the minimization problem be posed on a union of $k$ copies of ${\mathbb R}^n$, and let a stable configuration consist of disconnected pieces in these copies. Separated congruen…

Let $X$ be the market-condition process with inaccessible lower endpoint $\alpha$, let $M$ be its running maximum, and let $V(x,m)$ be the value function on the state space…

Let $X$ be the market-condition process, let $M$ be its running maximum, and let $V(x,m)$ be the value function. Let $b(m)$ denote the free boundary, with $min[underline m,\beta)$,…

Let $(u_{i,\beta})$ be a sequence of solutions satisfying the nontriviality condition that its limit profile is not identically zero. Suppose that $x_\beta\in\Gamma_\beta$ and…

Barles–Soner scaling conjecture. As $a\to 0$ and for both $p=2$ and $p=\infty$,

RAPM scaling conjecture. For both $p=2$ and $p=\infty$,

Convergence-rate conjecture. As $h\to 0^+$,