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2003, Mathematical Sciences Research Institute publications, ISBN 0521824699, Volume 47, xii, 400
Book
2013, Mathematical Sciences Research Institute publications, ISBN 1107032016, xii, 580
Book
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 01/2020
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 06/2019, Volume 126, pp. 273 - 291
We consider the partial data inverse boundary problem for the Schrödinger operator at a frequency on a bounded domain in , , with impedance boundary... 
Carleman estimates | High frequency limit | Partial data inverse problems | Stability estimates
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 7/2016, Volume 205, Issue 1, pp. 83 - 120
Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a... 
Mathematics, general | Mathematics | 35R30 | 35S05 | 53C65 | 53C21 | TENSOR-FIELDS | MATHEMATICS | Algorithms | Reconstruction | Geometry | Inverse problems | Convexity | Stripping | Transforms | X-rays | Geodesy | Boundaries
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2020, Volume 148, Issue 2, pp. 681 - 685
We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in \mathbb{R}^n, n\ge 2, for a class of... 
Journal Article
Bulletin of Mathematical Sciences, ISSN 1664-3607, 7/2014, Volume 4, Issue 2, pp. 209 - 279
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 7/2018, Volume 361, Issue 2, pp. 525 - 582
We study inverse boundary problems for magnetic Schrödinger operators on a compact Riemannian manifold with boundary of dimension ≥  3. In the first part of... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MANIFOLDS | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | EQUATION | UNIQUENESS | Magnetic fields | Anisotropy
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 03/2015, Volume 40, Issue 3, pp. 438 - 474
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 11/2013, Volume 365, Issue 11, pp. 5737 - 5758
with one measurement. We give sharp conditions for stability as well. An application to thermoacoustic tomography is also presented.]]> 
MATHEMATICS | INVERSE HYPERBOLIC PROBLEM | EXACT CONTROLLABILITY | STABILITY | GLOBAL UNIQUENESS | COEFFICIENTS | BOUNDARY | OBSERVABILITY | THERMOACOUSTIC TOMOGRAPHY | WAVE-EQUATIONS | UNIQUE CONTINUATION
Journal Article
Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 6/2012, Volume 109, Issue 26, pp. 10169 - 10174
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 11/2016, Volume 348, Issue 1, pp. 185 - 219
We extend a global uniqueness result for the Calderón problem with partial data, due to Kenig–Sjöstrand–Uhlmann (Ann. Math. (2) 165:567–591, 2007), to the case... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | GLOBAL UNIQUENESS | INVERSE PROBLEMS | LIPSCHITZ CONDUCTIVITIES | BOUNDARY MEASUREMENTS | LESS REGULAR CONDUCTIVITIES | PHYSICS, MATHEMATICAL
Journal Article
Journal of the American Mathematical Society, ISSN 0894-0347, 04/2016, Volume 29, Issue 2, pp. 299 - 332
The local results lead to a global lens rigidity uniqueness and stability result assuming that the manifold is foliated by strictly convex hypersurfaces.]]> 
TENSOR-FIELDS | TOMOGRAPHY | MATHEMATICS | LENS RIGIDITY | X-RAY TRANSFORM | NEGATIVE CURVATURE | STABILITY | METRICS | NONSIMPLE RIEMANNIAN-MANIFOLDS | INTEGRAL GEOMETRY PROBLEM | GEODESICS
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 6/2018, Volume 360, Issue 2, pp. 555 - 609
We consider inverse problems in space–time (M, g), a 4-dimensional Lorentzian manifold. For semilinear wave equations $${\square_g u + H(x, u) = f}$$... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | THEOREM | CAUCHY-PROBLEM | PROGRESSING WAVES | PHYSICS, MATHEMATICAL | SINGULAR SYMBOLS | OPERATORS | UNIQUE CONTINUATION
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 03/2015, Volume 40, Issue 3, pp. 438 - 474
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 03/2015, Volume 40, Issue 3, pp. 438 - 474
We prove uniform L super( )pestimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary,... 
Manifolds | Operators | Partial differential equations | Spectra | Boundaries | Estimates | Optimization
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 03/2015, Volume 40, Issue 3, pp. 438 - 474
We prove uniform L p estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing... 
Uniform estimate | 35J30 | Resolvent | 58J50 | Elliptic operator | Functional calculus
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 03/2015, Volume 40, Issue 3, p. 438
  We prove uniform L p estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary,... 
Partial differential equations | Estimates
Journal Article
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