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math.AP2014
Strichartz and Localized Energy Estimates for the Wave Equation in Strictly Concave Domains
Matthew D. Blair
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting t…
math.AP2014★ 30 cited
Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions
Matthew D. Blair, Christopher D. Sogge
We obtain some improved essentially sharp Kakeya-Nikodym estimates for eigenfunctions in two-dimensions. We obtain these by proving stronger related microlocal estimates involving…