5 problems

Optimal Newman-pole parameter conjecture. The value $\sigma=\sqrt{2(2-\beta)\beta}\,\pi$ is optimal for the Laplace problem. The authors report that it also works well for the modi…

Let $\Omega$ be a domain whose boundary $\partial\Omega$ is Lipschitz, possibly with a large Lipschitz constant, and let $E$ denote the relevant boundary zero Cauchy data set for a…

Let $u$ and $v$ satisfy the hypotheses of the preceding strong Laplace Hopf-lemma conjecture, including $u_t(0,0)=0$. Finite-order vanishing conjecture. If, in addition, $u(t,0)$ a…

Strong Laplace Hopf-lemma conjecture. If, in addition, $u_t(0,0)=0$, then

Consider a problem for the Laplace equation in an unbounded domain with multiple objects, each having either a Dirichlet or a Neumann condition imposed on its boundary. In this con…