Abstract
We consider the L p Hardy inequality involving the distance to the boundary for a domain in the n-dimensional Euclidean space. We study the dependence on p of the corresponding best constant and we prove monotonicity, continuity and differentiability results. The focus is on non-convex domains in which case such a constant is in general not explicitly known.
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Barbatis, G., Lamberti, P.D. Monotonicity, continuity and differentiability results for the L p Hardy constant. Isr. J. Math. 215, 1011–1024 (2016). https://doi.org/10.1007/s11856-016-1400-z
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DOI: https://doi.org/10.1007/s11856-016-1400-z