# Mathematische Nachrichten

## 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.

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