Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients

By Herbert Koch, D. Tataru. 2001

197 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aad3d0a515650c3f73cc0174ddca6795c2f1207c

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In Applied Mathematics

1. Carlos E. Kenig
2. Mikko Salo
3. D. Tataru
4. A. Ionescu
5. David dos Santos Ferreira
6. Herbert Koch
7. David Jerison
8. Giovanni Alessandrini

In Computational Theory and Mathematics

1. Mikko Salo
2. D. Tataru
3. David Jerison
4. A. Ionescu
5. David dos Santos Ferreira
6. Giovanni Alessandrini
7. Herbert Koch
8. Carlos E. Kenig

In Mathematical Physics

1. Carlos E. Kenig
2. Mikko Salo
3. A. Ionescu
4. D. Tataru
5. David dos Santos Ferreira
6. Herbert Koch
7. Terence Tao
8. Gunther Uhlmann

Citations in the corpus

• The stability for the Cauchy problem for elliptic equations (2009, background): “With no ambition of completeness, let us mention Hörmander [44], Jerison and Kenig [50], Garofalo and Lin [32, 33], Fabes, Garofalo and Lin [30] and, more recently, Koch and Tataru [55].”
• On the absence of positive eigenvalues of Schrödinger operators with rough potentials (2003, methodology): “for any p, a ∈ [1, ∞]. Such spaces were used in the recent work of Koch and Tataru [ KoTa1 ].”
• Dispersive estimates for principally normal pseudodifferential operators (2004, background): “For strong unique continuation problems and problems involving gradient potentials we refer the reader to Wolff [25], the authors paper [13], and the references therein.”
• Determining an Unbounded Potential from Cauchy Data in Admissible Geometries (2011, background): “Finally, if one allows strongly pseudoconvex Carleman weights then much stronger estimates are available (see for instance [12, 13, 21]), however for the applications to inverse problems it seems necessary to restrict to limiting Carleman weights.”
• L^p eigenfunction bounds for the Hermite operator (2004, background): “This was first observed in work of Jerison [6]; see also the authors paper [10] and further references therein.”
• Unique Continuation Problems for Partial Differential Equations (2004, background): “See also [7] for up to date references.”
• Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients (2007, methodology): “Finally, the authors’ article [18] combines the ideas above into a nearly optimal scale invariant ESUCP result for the elliptic problem, with (i) a Lipschitz metric g, (ii) an L n 2 potential V , and (iii) an almost L gradient potential W .”