| Abstract: |
| We consider the attainability of a maximizing problem associated with the Sobolev embedding. The existence and non-existence of a maximizer are related to the exponents appearing in the problem. Indeed, for some range
of the exponents, we have a non-existence result in spite of the sub-critical setting and the radial nature of the problem. In fact, we characterize the value which is the threshold in terms of the attainability of the problem. We also consider the attainability of the problem when the exponent becomes the threshold number with its computation of the exact value for some range of the exponents. This content is joint work with Prof. Michinori Ishiwata in Osaka University. |
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