On the Lp norm of spectral clusters for compact manifolds with boundary |
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Authors: | Hart F. Smith Christopher D. Sogge |
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Affiliation: | (1) Department of Mathematics, University of Washington, Seattle, WA 98195, USA;(2) Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA |
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Abstract: | We use microlocal and paradifferential techniques to obtain L 8 norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary. The result leads to optimal L q bounds, in the range 2⩽q⩽∞, for L 2 - normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds with boundary. We also establish new sharp L q estimates in higher dimensions for a range of exponents q̅n⩽q⩽∞. The authors were supported by the National Science Foundation, Grants DMS-0140499, DMS-0099642, and DMS-0354668. |
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