distance function, convex domain

Let Omega denote a bounded domain in R^n.


Does any one know what conditions can be put on Omega such that

- Delta d(x) >= c >0 in Omega (in the sense of distributions) ?


I think if Omega convex we have >=0.

What does strictly convex give us ?




Also are there any trivial methods to see any of these results?



thanks


craig
.

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