A dichotomy for complex Robin eigenvalues at large boundary parameter, with new numerical range bounds, a Dirichlet-to-Neumann proof, and interval, rectangle and ball asymptotics.
Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Let $\Omega \subset {\bf R}^d$ be a bounded open set with Lipschitz boundary $\Gamma$. It will be shown that the Jordan chains of m-sectorial second-order elliptic partial differential operators with measurable coefficients and (local or non-local) Robin boundary conditions in $L_2(\Omega)$ can be characterized with the help of Jordan chains of the Dirichlet-to-Neumann map and the boundary operator from $H^{1/2}(\Gamma)$ into $H^{-1/2}(\Gamma)$. This result extends the Birman--Schwinger principle in the framework of elliptic operators for the characterization of eigenvalues, eigenfunctions and geometric eigenspaces to the complete set of all generalized eigenfunctions and algebraic eigenspaces.
fields
math.SP 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
On the eigenvalues of the Robin Laplacian with a complex parameter
A dichotomy for complex Robin eigenvalues at large boundary parameter, with new numerical range bounds, a Dirichlet-to-Neumann proof, and interval, rectangle and ball asymptotics.