Abstract
We geometrically describe families of non-convex plane and spatial domains in which the basic Hardy inequality is valid with the constant 1/4. In our constructions we use some new constants depending on the dimension; we determine them as roots of Lamb-type equations. We also use the constant defined by E. B. Davies.
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Original Russian Text © F.G. Avkhadiev, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 9, pp. 59–63.
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Avkhadiev, F.G. Families of domains with best possible hardy constant. Russ Math. 57, 49–52 (2013). https://doi.org/10.3103/S1066369X13090077
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DOI: https://doi.org/10.3103/S1066369X13090077