8 problems

Consider compact contact sets arising from global solutions of the thin obstacle problem with higher-order growth. Nonconvexity-mechanism conjecture. Nonconvexity is achieved eithe…

Let $u$ be a global solution to the thin obstacle problem with a compact contact set, allowing general growth. General-growth nonconvexity conjecture. Not all compact contact sets…

Let $u$ be a global solution to the thin obstacle problem with cubic growth, and suppose that its positivity set on the thin space is bounded. Cubic positivity-set conjecture. The…

Let $u$ be a global solution to the thin obstacle problem with compact contact set and higher-order growth. Higher-order nonconvexity conjecture. Convexity of the contact set shoul…

Let $u$ be a global solution of the thin obstacle problem with superquadratic growth, and let its contact set on the thin space be compact. The compact-contact-set conjecture. Such…

Let $u$ be a global solution to the thin obstacle problem with at most quadratic growth, and let $\Lambda(u)$ denote its contact set. Suppose that $\Lambda(u)$ is compact. Conjectu…

Consider the Signorini problem, also known as the thin obstacle problem, and its free boundary. Generic smoothness conjecture. Generically, the free boundary in the Signorini probl…

Let $u$ be a solution to the thin obstacle problem, let $\Gamma(u)$ be its free boundary, and define … Thus, $\Gamma_*(u)$ consists of free-boundary points whose homogeneity is not…