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On Some Properties of Extremals in a Variational Problem Generated by the Sobolev Embedding Theorem

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Abstract

Some properties of extremal functions in the inequality \(\mathop {{\text{inf}}}\limits_{u \in W_p^1 (\Omega ),u \ne 0} \frac{{||u||W_p^1 (\Omega )}}{{||u||L_q (\Omega )}} >0\) are studied. Bibliography: 10 titles.

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Authors
  1. A. I. Nazarov
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  2. A. P. Scheglova
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Nazarov, A.I., Scheglova, A.P. On Some Properties of Extremals in a Variational Problem Generated by the Sobolev Embedding Theorem. Journal of Mathematical Sciences 120, 1125–1144 (2004). https://doi.org/10.1023/B:JOTH.0000014842.55031.98

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  • DOI: https://doi.org/10.1023/B:JOTH.0000014842.55031.98

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