Preprint, January 2010

Calculus of Variations and PDE's**39** (2010), 547-555.

Original article at doi:10.1007/s00526-010-0324-4

Citations on Google Scholar

Calculus of Variations and PDE's

Original article at doi:10.1007/s00526-010-0324-4

Citations on Google Scholar

Given a bounded domain Ω we look at the minimal
parameter Λ(Ω) for which a Bernoulli free
boundary value problem for the *p*-Laplacian has a
solution minimising an energy functional. We show that amongst
all domains of equal volume Λ(Ω) is minimal for
the ball. Moreover, we show that the inequality is sharp with
essentially only the ball minimising
Λ(Ω). This resolves a problem related to a
question asked in [Flucher et al., J. Reine
Angew. Math. **486**(1997), 165–204].

**AMS Subject Classification (2000):** 35R35, 49R05

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