2 problems

Kenig's conjecture. The spectral radius of $D'_{\Gamma}$ on $L^2_0(\Gamma)$ satisfies

Let $\Gamma$ be a piecewise $C^3$ Jordan curve with finitely many corners, whose angles lie strictly between $0$ and $\pi$. Let $K \colon H^{1/2}(\Gamma) \to H^{1/2}(\Gamma)$ be th…