Reflection principles for functions of Neumann and Dirichlet Laplacians on open reflection invariant subsets of ${\mathbb{R}}^d$

Jacek Małecki, Krzysztof Stempak

For an open subset $\Omega$ of ${\mathbb{R}}^d$, symmetric with respect to a hyperplane and with positive part ${\Omega }_{+}$, we consider the Neumann/Dirichlet Laplacians $-{\Delta }_{N/D,\Omega }$ and $-Δ_{N/D…