Extremals for sharp GNS inequalities on compact manifolds
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| 008 | 210128e20151001xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10231-014-0426-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0426-2 | ||
| 245 | 0 | 0 | |a Extremals for sharp GNS inequalities on compact manifolds |h [Elektronische Daten] |c [Emerson Abreu, Jurandir Ceccon, Marcos Montenegro] |
| 520 | 3 | |a Let $$(M,g)$$ ( M , g ) be a closed Riemannian manifold of dimension $$n \ge 2$$ n ≥ 2 . In Ceccon and Montenegro (Math Z 258:851-873, 2008; J Diff Equ 254(6):2532-2555, 2013) showed that, for any $$1 < p \le 2$$ 1 < p ≤ 2 and $$1 \le q < r < p^* = \frac{np}{n-p}$$ 1 ≤ q < r < p ∗ = n p n - p , there exists a constant $$B$$ B such that the sharp Gagliardo-Nirenberg inequality $$\begin{aligned} \left( \int _M |u|^r\; \mathrm{d}v_g \right) ^{\frac{p}{r \theta }} \le \left( A_{\mathrm{opt}} \int _M |\nabla _g u|^p\; \mathrm{d}v_g + B \int _M |u|^p\; \mathrm{d}v_g \right) \left( \int _M |u|^q\; \mathrm{d}v_g \right) ^{\frac{p(1 - \theta )}{\theta q}}. \end{aligned}$$ ∫ M | u | r d v g p r θ ≤ A opt ∫ M | ∇ g u | p d v g + B ∫ M | u | p d v g ∫ M | u | q d v g p ( 1 - θ ) θ q . holds for all $$u \in C^\infty (M)$$ u ∈ C ∞ ( M ) . In this work, assuming further $$1 < p < 2, p < r$$ 1 < p < 2 , p < r and $$1 \le q \le \frac{r}{r-p}$$ 1 ≤ q ≤ r r - p , we derive existence and compactness results of extremal functions corresponding to the saturated version of the above sharp inequality. Sobolev inequality can be seen as a limiting case as $$r$$ r tends to $$p^*$$ p ∗ . | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Sharp Sobolev inequalities |2 nationallicence | |
| 690 | 7 | |a De Giorgi-Nash-Moser estimates |2 nationallicence | |
| 690 | 7 | |a Extremal functions |2 nationallicence | |
| 690 | 7 | |a Compactness |2 nationallicence | |
| 700 | 1 | |a Abreu |D Emerson |u Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil |4 aut | |
| 700 | 1 | |a Ceccon |D Jurandir |u Departamento de Matemática, Universidade Federal do Paraná, Caixa Postal 019081, 81531-990, Curitiba, PR, Brazil |4 aut | |
| 700 | 1 | |a Montenegro |D Marcos |u Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1393-1421 |x 0373-3114 |q 194:5<1393 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0426-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0426-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Abreu |D Emerson |u Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ceccon |D Jurandir |u Departamento de Matemática, Universidade Federal do Paraná, Caixa Postal 019081, 81531-990, Curitiba, PR, Brazil |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Montenegro |D Marcos |u Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1393-1421 |x 0373-3114 |q 194:5<1393 |1 2015 |2 194 |o 10231 | ||