Displaying similar documents to “Sharp L p Carleman estimates and unique continuation”

Equivalent norms in some spaces of analytic functions and the uncertainty principle

Boris Paneah (1996)

Banach Center Publications

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The main object of this work is to describe such weight functions w(t) that for all elements f ∈ L p , Ω the estimate ∥ w f ∥ p ≥ K ( Ω ) ∥ f ∥ p is valid with a constant K(Ω), which does not depend on f and it grows to infinity when the domain Ω shrinks, i.e. deforms into a lower dimensional convex set Ω ∞ . In one-dimensional case means that K ( σ ) : = K ( Ω σ ) → ∞ as σ → 0. It should be noted that in the framework of the signal transmission problem such estimates describe a signal’s behavior under the influence of detection and amplification....

On the Fefferman-Phong inequality

Abdesslam Boulkhemair (2008)

Annales de l’institut Fourier

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We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by n 2 + 4 + ϵ improving thus the bound 2 n + 4 + ϵ obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type S 0 , 0 0 , we show that this number is bounded by n + 4 + ϵ ; more precisely, for a non negative symbol a , the Fefferman-Phong inequality holds if ∂ x α ∂ ξ β a ( x , ξ ) are bounded for, roughly, 4 ≤ | α | + | β | ≤ n + 4 + ϵ . To obtain such results and others, we first prove an abstract result which...

Oblique derivative problem for elliptic equations in non-divergence form with V M O coefficients

Giuseppe di Fazio, Dian K. Palagachev (1996)

Commentationes Mathematicae Universitatis Carolinae

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A priori estimates and strong solvability results in Sobolev space W 2 , p ( Ω ) , 1 < p < ∞ are proved for the regular oblique derivative problem ∑ i , j = 1 n a i j ( x ) ∂ 2 u ∂ x i ∂ x j = f ( x ) a.e. Ω ∂ u ∂ ℓ + σ ( x ) u = ϕ ( x ) on ∂ Ω when the principal coefficients a i j are V M O ∩ L ∞ functions.

Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions

Jérôme Le Rousseau, Nicolas Lerner (2010)

Journées Équations aux dérivées partielles

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We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are necessary.

L p - L q -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Jerzy Gawinecki (1991)

Annales Polonici Mathematici

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We prove the L p - L q -time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the L p - L q -time decay estimates.

Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms

Viviane Baladi, Masato Tsujii (2007)

Annales de l’institut Fourier

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We study spectral properties of transfer operators for diffeomorphisms T : X → X on a Riemannian manifold X . Suppose that Ω is an isolated hyperbolic subset for T , with a compact isolating neighborhood V ⊂ X . We first introduce Banach spaces of distributions supported on V , which are anisotropic versions of the usual space of C p functions C p ( V ) and of the generalized Sobolev spaces W p , t ( V ) , respectively. We then show that the transfer operators associated to  T and a smooth weight g extend boundedly to these...