The best constant in a sobolev inequality: Applicable Analysis: Vol 41, No 1-4

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Abstract

The best constant in the Sobolev inequality

is shown to be given by a quantity in terms of the solution of an elliptic boundary value problem, where,

j is a measurable open subset,

with a positive measure, and

Some examples are presented with either an analytic expression or a numerical value for the best constant.

AMS(MOS):

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The best constant in a sobolev inequality

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