From semiclassical Strichartz estimates to uniform $L^p$ resolvent estimates on compact manifolds
| Autor: | Nicolas Burq, David Dos Santos Ferreira, Katya Krupchyk |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Irvine], University of California [Irvine] (UCI), University of California-University of California, ANR-13-JS01-0006,iproblems,Problèmes Inverses(2013), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), University of California [Irvine] (UC Irvine), University of California (UC)-University of California (UC) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
47A10
58J50 81Q20 General Mathematics Operator (physics) 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Boundary (topology) Semiclassical physics Riemannian manifold 01 natural sciences Mathematics - Spectral Theory Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Spectral analysis 010307 mathematical physics 0101 mathematics Laplace operator Spectral Theory (math.SP) Mathematics Resolvent Analysis of PDEs (math.AP) |
| Zdroj: | International Mathematics Research Notices International Mathematics Research Notices, Oxford University Press (OUP), 2018, 2018 (16), pp.5178-5218. ⟨10.1093/imrn/rnx042⟩ International Mathematics Research Notices, 2018, 2018 (16), pp.5178-5218. ⟨10.1093/imrn/rnx042⟩ |
| ISSN: | 1073-7928 1687-0247 |
| DOI: | 10.1093/imrn/rnx042⟩ |
| Popis: | International audience; We prove uniform $L^p$ resolvent estimates for the stationary damped wave operator. The uniform $L^p$ resolvent estimates for the Laplace operator on a compact smooth Riemannian manifold without boundary were first established by Dos Santos Ferreira-Kenig-Salo and advanced further by Bourgain-Shao-Sogge-Yao. Here we provide an alternative proof relying on the techniques of semiclassical Strichartz estimates. This approach allows us also to handle non-self-adjoint perturbations of the Laplacian and embeds very naturally in the semiclassical spectral analysis framework. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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