4 problems

Let $\Omega\subset\mathbb{R}^N$ be a domain and consider weak solutions of … Assume that the coefficient matrix satisfies … for $\xi\in\mathbb{R}^N$ and almost every $x\in\Omega$,…

Optimal growth rate conjecture. The optimal growth rate estimate given in Theorem holds if and only if $\gamma<2$ (thus $\theta<\frac{3\pi}{2}$).

Let $\Omega$ be the domain, let $f\in L^1(\Omega)$ be nonnegative, and let $u$ be a solution of the singular elliptic problem … with homogeneous Dirichlet boundary condition $u=0$…

Existence conjecture. The problem has a solution for every $\lambda>0$ under this almost critical assumption.