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Title of Journal: Calc Var

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Abbravation: Calculus of Variations and Partial Differential Equations

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Springer Berlin Heidelberg

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DOI

10.1007/bf01058313

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1432-0835

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Singular points of Hölder asymptotically optimally

Authors: Stephen Lewis
Publish Date: 2015/09/03
Volume: 54, Issue: 4, Pages: 3667-3713
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Abstract

We consider the question of how the doubling characteristic of a measure determines the regularity of its support The question was considered by David et al Commun Pure Appl Math 54385–449 2001 for codimension 1 under a crucial assumption of flatness and later by Preiss et al Calc Var PDE’s 35339–363 2009 in higher codimension However these studies leave open the question of what can be said about the geometry of the support of such measures in a neighborhood about a nonflat point Here we answer the question for codimension1 Hölder doubling measures in mathbb R4 by constructing parametrizations in a neighborhood of a nonflat point by the Kowalski–Preiss cone These parametrizations extend to be C1beta diffeomorphisms on an open set Some of our parametrization techniques build on ideas from David et al Mem AMS 215 2012 Commun Pure Appl Math 54385–449 2001 Preiss et al Calc Var PDE’s 35339–363 2009 and Taylor Annals Math 103489–539 1976

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  2. Fractional Poincaré inequality with finite total Q -curvature
  3. Solitary waves for a class of quasilinear Schrödinger equations in dimension two
  4. Thick clusters for the radially symmetric nonlinear Schrödinger equation
  5. On elliptic systems with Sobolev critical growth
  6. Critical points for functionals with quasilinear singular Euler–Lagrange equations
  7. Duality for rectified cost functions
  8. An approach to minimization under a constraint: the added mass technique
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  14. On Newton equations which are totally integrable at infinity
  15. Energy asymptotics for Type II superconductors
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  18. Cahn–Hilliard–Navier–Stokes systems with moving contact lines
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