Abstract
We use microlocal and paradifferential techniques to obtain L8 norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary. The result leads to optimal Lq bounds, in the range 2⩽q⩽∞, for L2 - normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds with boundary. We also establish new sharp Lq estimates in higher dimensions for a range of exponents q̅n⩽q⩽∞.
Funding Statement
The authors were supported by the National Science Foundation, Grants DMS-0140499, DMS-0099642, and DMS-0354668.
Citation
Hart F. Smith. Christopher D. Sogge. "On the Lp norm of spectral clusters for compact manifolds with boundary." Acta Math. 198 (1) 107 - 153, 2007. https://doi.org/10.1007/s11511-007-0014-z
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