Sobolev norms
Growth of Sobolev norms for linear Schrödinger operators
... This result is the analogous to [10, 13] in which similar bounds are obtained for the linear Schr¨ odinger equation with time-dependent potential, but in our case the proof is much simpler. The result of Theorem 2.4 ...
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Growth of Sobolev norms for coupled Lowest Landau Level equations
... the Sobolev norms. A growth of Sobolev norm corresponds to a transfer of energy from low to high frequencies, but in the Bargmann-Fock space E, this is equivalent to a transfer in the physical space, ...
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1-D QUANTUM HARMONIC OSCILLATOR WITH TIME QUASI-PERIODIC QUADRATIC PERTURBATION: REDUCIBILITY AND GROWTH OF SOBOLEV NORMS
... • Boundedness w.r.t. t is always true for “most” E ∈ I. • For “generic” time-dependent perturbation, polynomial growth and expo- nential growth to infinity w.r.t. t occur for E in a “small” part of I. Concrete examples ...
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On time dependent Schrödinger equations: global well-posedness and growth of Sobolev norms
... In same cases better estimates on the H r k -norm of the flow are known. For example if V (t, x) is a quasi-periodic function of time and small in size, one might try to prove reducibility, which in turn implies that the ...
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Beating effects in cubic Schrödinger systems and growth of Sobolev norms
... where ( ˆ f j ) j∈Z denote the Fourier coefficients of f . We then define a semi-norm kf k G α as the best constant K in (1.9) (see [11] for more details). The beating phenomenon then leads to the growth of ...
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Quasi invariant modified Sobolev norms for semi linear reversible PDEs.
... We also notice that for the same class of reversible systems we can prove a Birkhoff normal form theorem that in turn implies the same bounds on the Sobolev norms. Nevertheless the technics that we use to ...
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Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations
... In this paper, the authors exhibit the existence of smooth solutions of the cubic defocusing nonlinear Schradinger equation on T2, whose H" norm is arbitrarily s[r] ...
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Small Ball Estimates for Quasi-Norms
... This suggest that small ball estimates are related to weighted norms of ˆ f X which are in turn known to be related to smoothness properties of f X . First, we consider vectors with independent coordinates and ...
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Norms for standard neuropsychological tests from the French CONSTANCES cohort: Norms for five neuropsychological tests
... Discussion This study provides updated and reliable norms for five neuropsychological tests broadly used in clinical practice for adults aged 45–70. First, the results illustrate the effect of age in almost all ...
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Sobolev algebras through Heat kernel estimates
... is an algebra for the pointwise product for all 1 < p < +∞ and α > 0 such that αp > n. This result is due to Strichartz in [63], where the Sobolev norm was shown to be equivalent to the L p -norm of a ...
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Differential of metric valued Sobolev maps
... The very first step to tackle in order to write down ( 1.1 ) is to understand what “d f” is. As stated, this is our goal in this manuscript. Let us informally describe the key concept in this work (the precise definitions ...
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Some remarks on weighted logarithmic Sobolev inequality
... logarithmic Sobolev inequality (or more generally F -Sobolev inequality): the Super weighted Poincar´e inequality; (2) use Lyapunov condition to prove these Super weighted Poincar´e inequalities; (3) show ...
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Compact Sobolev embeddings and torsion functions
... (French) [Functional analysis] Th´ eorie et applications. [Theory and applications]. Collection Math´ ematiques Appliqu´ ees pour la Maˆıtrise. [Collection of Applied Mathematics for the[r] ...
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Generalized logarithmic Hardy-Littlewood-Sobolev inequality
... [4] Blanchet, A., Dolbeault, J., and Perthame, B. (2006). Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions. Electron. J. Differential Equations, 44:1–33. [5] Campos, ...
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X-Ray Sobolev Variational Auto-Encoders
... On the other hand there is the remarkable work on the energy distance by Szekely and al. (see [ 22 ] and related references) that establish an encouraging framework; at the contrary of the first group cited, here the ...
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LegalRuleML: XML-based rules and norms
... This part of metadata is modeled to allow a multiple annotation of the rules coming from different authors. In the legal domain it is common to find different interpreta- tions of the norms and equally legitimate ...
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Social Norms and Rationality of Choice
... external norms are taken into consideration by specifying all pairs consisting of a feasible set and an element of this set with the interpretation that this element is prohibited from being chosen from this set ...
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Modified logarithmic Sobolev inequalities and transportation inequalities
... [Mau91℄ B. Maurey . Some deviation inequalities. Geom. Fun
t. Anal., 1(2):188{197, 1991. [OV00℄ F. Otto and C. Villani. Generalization of an inequality by Talagrand, and links with the logarithmi Sobolev ...
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Facts, Norms and Expected Utility Functions
... , NORMS AND EXPECTED UTILITY FUNCTIONS Sophie Jallais, Pierre-Charles Pradier & David Teira ∗ ABSTRACT In this paper we want to explore an argumentative pattern that provides a normative justification for ...
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Absolute norms of $p$-primary units
... Abstract. We prove a local analogue of a theorem of J. Mar- tinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a state- ment about 2-primary ...
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