Dispersive estimates for principally normal pseudodifferential operators

By Herbert Koch, D. Tataru. 2004

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In this article we construct parametrices and obtain dispersive estimates for a large class of principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used to prove Lq Carleman inequalities, which in turn yield unique continuation results for various partial differential operators with rough potentials. © 2004 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/da0b6b473ead1ce9c345afbd3b6cf48140344d09

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions (2009, background): “These spaces were first introduced in unpublished work of the second author, and have proved their usefulness as scale invariant substitutes of X 1 2 type spaces in several problems, see [11], [12], [5], [2].”
On Lp resolvent estimates for Laplace–Beltrami operators on compact manifolds (2011, methodology): “We use ideas coming from [14] and also [2, 3] to deal with the remainder terms.”
Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients (2007, background): “This immediately (see also [19]) leads to Strichartz estimates for the solution to the inhomogeneous equation ivt −Hv = g v 0 = v0 namely v Lp 0 2 Lq v0 L2 + g Lp′ 0 2 Lq′ (4.”
Global parametrices and dispersive estimates for variable coefficient wave equations (2007, background): “In the finite time analysis in [15], [36] the evolution is turned into a transport equation in the phase space modulo small errors.”
Global Schrödinger maps in dimensions $d≥ 2$: Small data in the critical Sobolev spaces (2011, methodology): “They have been successfully used for instance in [27], [26], [4], and [10].”
On the Lp norm of spectral clusters for compact manifolds with boundary (2006, methodology): “Then, following Koch-Tataru [7] we define ‖ũ‖(2)V 2 q = ‖ũ(0, · )‖ 2 L2(R4) + sup P ∑”
Bilinear Strichartz estimates for the Zakharov–Kuznetsov equation and applications (2013, methodology): “We start by recalling the definition of the function spaces U(2) and V 2 (see [9] and [6]).”
Parametrices and dispersive estimates for Schrödinger operators with variable coefficients (2008, methodology): “Rescaling Q to a cube of size 1 × ( √ r)n we match the parametrix constructions in [25], [14].”
Strichartz estimates and local smoothing estimates for asymptotically flat Schr (2007, unknown): “We also refer the interested reader to the simplified approaches of [15] and [27].”