5 problems

Let $\Omega\subset\mathbb{C}^n$ be the strictly pseudoconvex domain and let $u_0$ be the initial datum considered in Theorem. Replace the assumption … by the condition that $u_0$ h…

Non-local modulus of continuity conjecture. Then $\varphi(\cdot,t)$ is a modulus of continuity for $u(\cdot,t)$ on $\Omega\times[0,\infty)$. This proposes that the higher-dimension…

Let $(M,g)$ be a complete, $n$-dimensional Riemannian manifold with bounded geometry. An ancient, positive solution is a positive solution $u$ of … that is defined for all past tim…

Let $\rho$ be a solution to the porous medium equation on $[-1,0] \times B_2(0)$. Assume that there is a nonempty open cone $C$ such that $\rho(t,x) \leq \rho(t,y)$ whenever…

Existence and uniqueness claim. The problem has a unique viscosity solution $u$.