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On the rate of change of the sharp constant in the Sobolev–Poincaré inequality
Abstract:The rate of change of the sharp constant in the Sobolev–Poincaré or Friedrichs inequality is estimated for a Euclidean domain that moves outward. The key ingredients are a Hadamard variation formula and an inequality that reverses the usual Hölder inequality.
Keywords:Sobolev–  Poincaré   inequality  Hadamard variation  Reverse Hö  lder inequality  35J20  35P30  46E35
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