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Optimal boundary holes for the Sobolev trace constant
Optimal boundary holes the Sobolev trace constant
2010/11/18
In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient $\|u\|_{W^{1,p}(\Omega)}^p / \|u\|_{L^q(\partial\Omega)}^p$ among functions that vanish in a set contained on the b...
Trace formula for dielectric cavities II: Regular, pseudo-integrable, and chaotic examples
Trace formula dielectric cavities Regular pseudo-integrable chaotic examples
2010/12/16
Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [PRE 78, 056202 (2008), Ref. [3]] the trace formula f...
Trace Functionals of the Kontsevich Quantization
Trace Functionals Kontsevich Quantization
2010/10/29
We generalize the notion of trace to the Kontsevich quantization algebra and show that for all Poisson manifolds representable by quotients of a symplectic manifold by a Hamiltonian action of a nilpo...