标题： 关于诺伊曼-庞加莱算子和自伴传输问题 显示英文标题

标题： On Neumann-Poincaré operators and self-adjoint transmission problems

摘要： 我们讨论在$L^2$设置下，作用于$-\nabla\cdot h\nabla$的算子的自伴性，其中分段常数函数$h$沿 Lipschitz 超曲面$\Sigma$有跳跃，而无需对$h$的符号做出显式假设。 我们建立了一系列充分条件，以$H^{\frac{3}{2}}$正则性来表述算子的自伴性，这些条件涉及跳跃值以及$\Sigma$的正则性和几何特性。 一个重要的中间步骤是与在$\Sigma$上的Neumann-Poincaré算子的Fredholm性质之间的联系，这在Lipschitz情况下是新的。 显示英文摘要

摘要： We discuss the self-adjointness in $L^2$-setting of the operators acting as $-\nabla\cdot h\nabla$, with piecewise constant functions $h$ having a jump along a Lipschitz hypersurface $\Sigma$, without explicit assumptions on the sign of $h$. We establish a number of sufficient conditions for the self-adjointness of the operator with $H^{\frac{3}{2}}$-regularity in terms of the jump value and the regularity and geometric properties of $\Sigma$. An important intermediate step is a link with Fredholm properties of the Neumann-Poincar\'e operator on $\Sigma$, which is new for the Lipschitz setting.