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Title of Journal: Math Ann

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Abbravation: Mathematische Annalen

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Springer Berlin Heidelberg

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1432-1807

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The NSLUC property and Klee envelope

Authors: A Jourani L Thibault D Zagrodny
Publish Date: 2015/08/29
Volume: 365, Issue: 3-4, Pages: 923-967
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Abstract

A notion called norm subdifferential local uniform convexity NSLUC is introduced and studied It is shown that the property holds for all subsets of a Banach space whenever the norm is either locally uniformly convex or kfully convex The property is also valid for all subsets of the Banach space if the norm is KadecKlee and its dual norm is Gâteaux differentiable off zero The NSLUC concept allows us to obtain new properties of the Klee envelope for example a connection between attainment sets of the Klee envelope of a function and its convex hull It is also proved that the Klee envelope with unit power plus an appropriate distance function is equal to some constant on an open convex subset as large as we need As a consequence of obtained results the subdifferential properties of the Klee envelope can be inherited from subdifferential properties of the opposite of the distance function to the complement of the bounded convex open set Moreover the problem of singleton property of sets with unique farthest point is reduced to the problem of convexity of Chebyshev sets

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  1. Estimates of the Green function for X-elliptic operators
  2. Fibred multilinks and singularities $${f \overline g}$$
  3. Hölder estimates for parabolic p ( x , t )-Laplacian systems
  4. Ricci flow on surfaces with cusps
  5. A non-laminar dynamical Green current
  6. Artin characters, Hurwitz trees and the lifting problem
  7. Generic non-selfadjoint Zakharov–Shabat operators
  8. Strichartz estimates via the Schrödinger maximal operator
  9. Examples of relative deformation spaces that are not locally connected
  10. Polynomial approximation of Berkovich spaces and definable types
  11. Prographes sylvestres et groupes profinis presque libres
  12. Zone diagrams in Euclidean spaces and in other normed spaces
  13. A critical radius for unit Hopf vector fields on spheres
  14. Many triangulated 3-spheres
  15. New examples of c 0 -saturated Banach spaces
  16. Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle
  17. Relatively weakly open sets in closed balls of Banach spaces, and real JB * -triples of finite rank
  18. The Bergman metric on complete Kähler manifolds
  19. Conformal dimension via subcomplexes for small cancellation and random groups
  20. Analytic torsion of Hirzebruch surfaces
  21. Déformations des cônes de vecteurs primitifs
  22. Radial entire solutions for supercritical biharmonic equations
  23. Weighted Calderón–Zygmund and Rellich inequalities in $$L^p$$
  24. On entropy, regularity and rigidity for convex representations of hyperbolic manifolds
  25. Rigidity of proper holomorphic maps between bounded symmetric domains
  26. On CR Paneitz operators and CR pluriharmonic functions
  27. Absence of wandering domains for some real entire functions with bounded singular sets
  28. Isomonodromic deformations of logarithmic connections and stability
  29. Pointwise equidistribution with an error rate and with respect to unbounded functions
  30. On the Frobenius stable part of Witt vector cohomology
  31. Quantitative mixing results and inner functions
  32. Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation
  33. Spin curves and Scorza quartics
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  37. On Oliver’s p -group conjecture: II
  38. Scattering in the energy space for the NLS with variable coefficients
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