A Geometric Characterization of a Sharp Hardy Inequality
نویسندگان
چکیده
In this paper, we prove that the distance function of an open connected set in R with a C boundary is superharmonic in the distribution sense if and only if the boundary is weakly mean convex. We then prove that Hardy inequalities with a sharp constant hold on weakly mean convex C domains. Moreover, we show that the weakly mean convexity condition cannot be weakened. We also prove various improved Hardy inequalities on mean convex domains along the line of Brezis-Marcus [7].
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