5 problems

Let $D\subset\mathbb{R}^3$ be an elastic inclusion, and let the Lamé parameters be … where $\chi_D$ is the characteristic function of $D$. The parameters $\epsilon_1\lambda_0$ and…

ALR-busting source conjecture. There exist $\delta_{\gamma}>0$ and $C_{\gamma}>0$ such that $E_{\delta}(a)\le C_{\gamma}$ for all $0<\delta\le\delta_{\gamma}$. The conjecture propo…

Let $0<\gamma<\gamma_*$. Consider sources $f\in L^2(\mathcal{M})$ with compact support or distributional sources such as dipoles, and let $E_{\delta}(\xi)$ and $V(x,y)$ denote the…

Suppose $0<\gamma<\gamma_*$, and let $1<p^1_{\gamma}<p^2_{\gamma}$ be the roots of $g_0(p;\gamma)$. Define $M_{\delta}(p;\gamma)$ as in the source. The numerator noncancellation co…

Let $g_0(p;\gamma)$ have roots $1<p^1_{\gamma}<p^2_{\gamma}$, with $0<\gamma<\gamma_*$. The order-$\delta$ behavior conjecture. The quantities $|g_{\delta}(p^1_{\gamma};\gamma)|$ a…