The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.
Inverse positivity for general Robin pr oblems on Lipschitz domains
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Stability of semigroup smoothing under relatively bounded perturbations yields spectral and eventually positive perturbation theorems for elliptic PDEs.
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Spectral properties of the Dirichlet-to-Neumann map for the Helmholtz equation
The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.
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Smoothing of operator semigroups under relatively bounded perturbations
Stability of semigroup smoothing under relatively bounded perturbations yields spectral and eventually positive perturbation theorems for elliptic PDEs.