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Apr 14, 2017 at 8:49 comment added Paul Bryan I've been told that a counter example to a lower bound in the case no convexity of $\Omega$ is assumed is given by two balls joined by a thin neck. Perhaps this is similar to the double well potential? But note here the problem is with the domain and not the potential.
Apr 12, 2017 at 1:41 comment added Paul Bryan Without the convexity assumption, is such a bound on the gap possible?
Apr 12, 2017 at 0:53 vote accept Math604
Apr 10, 2017 at 7:00 comment added Paul Bryan Yes, sorry it does.
Apr 10, 2017 at 6:29 comment added Carlo Beenakker doesn't this assume convex $\Omega$?
Apr 10, 2017 at 1:45 history answered Paul Bryan CC BY-SA 3.0