7 problems

Let $\Omega\subset\mathbb{R}^{\mathfrak{n}}$ be a domain with Ahlfors regular boundary of dimension $\mathfrak{d}$, in the lower codimensional case … Assume the hypotheses of Theor…

Let $\Omega$ be a domain satisfying the ellipticity and geometric hypotheses used in the paper for the Poisson problem, including an unbounded complement and, as appropriate, the w…

Consider the Poisson problem … with solution $u^*\in H^t_0$, forcing term $\xi\in H^{-s}$, and reproducing-kernel Hilbert space $\mathcal{H}_K=H^q$ for some $q>t$, where $t=2-s$. L…

Poisson tau-method solvability conjecture. If $f\in\Pi_N^d$ and the tau polynomials $P_k$ span $\Pi_{N-2,N}^{(d)}$, then the tau-modified equation

Saint-Venant's conjecture. Among all such domains, the solution $u$ assumes its largest maximum when $\Omega$ is a ball.

Let a hypersphere and a plane stereographically connected to it be given, and consider solutions of the Poisson equation on each of these spaces. Stereographic correspondence conje…

Conjectured sharp-constant formulas. The constants $A_p$ and $B_p$ satisfy