6533b7d8fe1ef96bd126a68a
RESEARCH PRODUCT
On Lp resolvent estimates for Laplace–Beltrami operators on compact manifolds
David Dos Santos FerreiraCarlos E. KenigMikko Salosubject
Hadamard parametrixLaplace–Beltrami operatorMathematics::Analysis of PDEsresolventoscillatory integralsMathematics::Spectral TheoryCarleman estimatesdescription
In this article we prove Lp estimates for resolvents of Laplace–Beltrami operators on compact Riemannian manifolds, generalizing results of Kenig, Ruiz and Sogge (1987) in the Euclidean case and Shen (2001) for the torus. We follow Sogge (1988) and construct Hadamard's parametrix, then use classical boundedness results on integral operators with oscillatory kernels related to the Carleson and Sjölin condition. Our initial motivation was to obtain Lp Carleman estimates with limiting Carleman weights generalizing those of Jerison and Kenig (1985); we illustrate the pertinence of Lp resolvent estimates by showing the relation with Carleman estimates. Such estimates are useful in the construction of complex geometrical optics solutions to the Schrödinger equation with unbounded potentials, an essential device for solving anisotropic inverse problems. peerReviewed
year | journal | country | edition | language |
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2014-01-01 |