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Invisible obstacles

A. G. Ramm (2007)

Annales Polonici Mathematici

It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.

Iterated oscillation criteria for delay partial difference equations

Başak Karpuz, Özkan Öcalan (2014)

Mathematica Bohemica

In this paper, by using an iterative scheme, we advance the main oscillation result of Zhang and Liu (1997). We not only extend this important result but also drop a superfluous condition even in the noniterated case. Moreover, we present some illustrative examples for which the previous results cannot deliver answers for the oscillation of solutions but with our new efficient test, we can give affirmative answers for the oscillatory behaviour of solutions. For a visual explanation of the examples,...

Iterative methods for parabolic functional differential equations

Milena Matusik (2013)

Applicationes Mathematicae

This paper is concerned with iterative methods for parabolic functional differential equations with initial boundary conditions. Monotone iterative methods are discussed. We prove a theorem on the existence of solutions for a parabolic problem whose right-hand side admits a Jordan type decomposition with respect to the function variable. It is shown that there exist Newton sequences which converge to the solution of the initial problem. Differential equations with deviated variables and differential...

Killing spinor-valued forms and the cone construction

Petr Somberg, Petr Zima (2016)

Archivum Mathematicum

On a pseudo-Riemannian manifold 𝕄 we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on 𝕄 and parallel fields on the metric cone over 𝕄 for spinor-valued forms.

Kneser-type theorem for the Darboux problem in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.

L p -Estimates for linear elliptic systems with discontinuous coefficients

Filippo Chiarenza, Michelangelo Franciosi, Michele Frasca (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this Note we give L p estimates 1 < p < + for the highest order derivatives of an elliptic system in non-divergence form with coefficients in VMO.

L p -inequalities for the laplacian and unique continuation

W. O. Amrein, A. M. Berthier, V. Georgescu (1981)

Annales de l'institut Fourier

We prove an inequality of the type | x | r f L p ( R n ) c ( n , p , q , r ) | x | τ + μ Δ f L q ( R n ) . This is then used to derive the unique continuation property for the differential inequality | Δ f ( x ) | | v ( x ) | | f ( x ) | under suitable local integrability assumptions on the function v .

Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications

Éric Gautier (2005)

ESAIM: Probability and Statistics

Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is also...

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