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  • 1. Filippas, S
    et al.
    Maz´ya, Vladimir G.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Tertikas, A
    Sharp Hardy-Sobolev inequalities2004In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 339, no 7, p. 483-486Article in journal (Refereed)
    Abstract [en]

    Let Omega be a smooth bounded domain in R-N, N greater than or equal to 3. We show that Hardy's inequality involving the distance to the boundary, with best constant (1/4), may still be improved by adding a multiple of the critical Sobolev norm.

  • 2.
    Kozlov, Vladimir
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Nazarov, Sergei A.
    St Petersburg State University, Russia; St Petersburg State Polytech University, Russia; Institute Problems Mech Engn RAS, Russia.
    Orlof, Anna
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Trapped modes supported by localized potentials in the zigzag graphene ribbon2016In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 354, no 1, p. 63-67Article in journal (Refereed)
    Abstract [en]

    Localized potentials in the Dirac equation for the electron dynamics in a zigzag graphene ribbon are constructed to support trapped modes while the corresponding eigenvalues are embedded into the continuous spectrum. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

  • 3.
    Liu, Zhenxia
    et al.
    Blåeldsvägen 12B, Sturefors, Sweden.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Probabilities of hitting a convex hull2014In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 352, no 11, p. 935-940Article in journal (Refereed)
    Abstract [en]

    In this note, we consider the non-negative least-square method with a random matrix. This problem has connections with the probability that the origin is not in the convex hull of many random points. As related problems, suitable estimates are obtained as well on the probability that a small ball does not hit the convex hull.

  • 4.
    Maz´ya, Vladimir G.
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Movchan, A.
    Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, United Kingdom.
    Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains2006In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 343, no 3, p. 185-190Article in journal (Refereed)
    Abstract [en]

    Asymptotic formulae for Green's kernels Ge (x, y) of various boundary value problems for the Laplace operator are obtained in regularly perturbed domains and certain domains with small singular perturbations of the boundary, as e ? 0. The main new feature of these asymptotic formulae is their uniformity with respect to the independent variables x and y. To cite this article: V. Maz'ya, A. Movchan, C. R. Acad. Sci. Paris, Ser. I 343 (2006). © 2006 Académie des sciences.

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