We investigate a natural approximation by subcritical Sobolev embeddings of the Sobolev quotient for the fractional Sobolev spaces Hs for any 0 < s < N/2, using Γ-convergence techniques. We show that, for such approximations, optimal functions always exist and exhibit a concentration effect of the Hs energy at one point.
Subcritical approximation of a Yamabe type non local equation: a Gamma-convergence approach / G., Palatucci; Pisante, Adriano; Y., Sire. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - 14:3(2015), pp. 819-840. [10.2422/2036-2145.201302_006]
Subcritical approximation of a Yamabe type non local equation: a Gamma-convergence approach
PISANTE, Adriano;
2015
Abstract
We investigate a natural approximation by subcritical Sobolev embeddings of the Sobolev quotient for the fractional Sobolev spaces Hs for any 0 < s < N/2, using Γ-convergence techniques. We show that, for such approximations, optimal functions always exist and exhibit a concentration effect of the Hs energy at one point.File allegati a questo prodotto
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