4 problems

Chen–Véron conjecture. In dimensions $1$ and $2$, such a fundamental solution exists, is radial and locally integrable, and satisfies the displayed bound.

Let $E(t,x,y)$ be the fundamental solution of a Schrödinger equation with a super-quadratic potential $V$ in spatial dimension $d$, and suppose that the one-dimensional result of Y…

Fundamental-solution conjecture. The fundamental solution $\Phi_{\ln}$ exists for $N=1,2$ and satisfies

Fundamental-solution conjecture. The candidate function $\mathsf S_{R,\beta}^{d,-}(\mathbf x,\mathbf x^\prime)$ is a fundamental solution for the Helmholtz operator…