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Uniform resolvent convergence for a strip with fast oscillating boundary
Uniform resolvent convergence strip fast oscillating boundary Analysis of PDEs
2012/6/30
In a planar infinite strip with fast periodically oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small. On the oscillatin...
From resolvent estimates to damped waves
resolvent estimates damped waves Analysis of PDEs
2012/6/29
In this paper we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of the dynamics near the un-damped set. We show that if r...
Semiclassical resolvent estimates at trapped sets
Resolvent estimates trapping propagation of singularities
2012/6/21
We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-trapping estimates in t...
Extending cutoff resolvent estimates via propagation of singularities
cutoff resolvent estimates propagation of singularities Analysis of PDEs
2011/9/9
Abstract: We use a gluing method developed in joint work with Andr\'as Vasy to show that polynomially bounded cutoff resolvent estimates at the real axis imply, up to a constant factor, the same estim...
Spectral estimates for resolvent differences of self-adjoint elliptic operators
Spectral estimates resolvent differences
2011/2/24
The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations.