6533b85bfe1ef96bd12ba21d
RESEARCH PRODUCT
On $L^p$ resolvent estimates for Laplace-Beltrami operators on compact manifolds
David Dos Santos FerreiraCarlos E. KenigMikko Salosubject
Pure mathematicsLaplace transformParametrixApplied MathematicsGeneral MathematicsMathematics::Analysis of PDEsTorusInverse problemAbsolute continuityMathematics::Spectral TheoryMathematics - Analysis of PDEsLaplace–Beltrami operatorEuclidean geometryFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]ResolventMathematicsAnalysis of PDEs (math.AP)description
Abstract. 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-12-14 |