By Li Y.Y., Ricciardi T.

**Read or Download A sharp Sobolev inequality on Riemannian manifolds PDF**

**Best mathematics books**

**Periodic solutions of nonlinear wave equations with general nonlinearities**

Authored by means of prime students, this entire, self-contained textual content provides a view of the state-of-the-art in multi-dimensional hyperbolic partial differential equations, with a selected emphasis on difficulties within which smooth instruments of study have proved valuable. Ordered in sections of steadily expanding levels of trouble, the textual content first covers linear Cauchy difficulties and linear preliminary boundary price difficulties, sooner than relocating directly to nonlinear difficulties, together with surprise waves.

**Chinese mathematics competitions and olympiads: 1981-1993**

This publication includes the issues and suggestions of 2 contests: the chinese language nationwide highschool pageant from 198182 to 199293, and the chinese language Mathematical Olympiad from 198586 to 199293. China has an exceptional checklist within the overseas Mathematical Olympiad, and the booklet comprises the issues which have been used to spot the crew applicants and choose the chinese language groups.

- International Mathematical Olympiads 1959-2000
- The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (Dover Books on Mathematics)
- Uncertainty Quantification and Stochastic Modeling with MATLAB
- The Witt Group of Degree k Maps and Asymmetric Inner Product Spaces (Lecture Notes in Mathematics)
- Mathematics of Classical & Quantum Physics, Vol. 1 (Addison-Wesley Series in Advanced Physics) by F. W. Byron (1969-01-03)
- The Mathematics of Knots: Theory and Application: 1 (Contributions in Mathematical and Computational Sciences)

**Additional resources for A sharp Sobolev inequality on Riemannian manifolds**

**Sample text**

When n = 6 and r = r¯ = 3/2, we have: U 2∗ ,µ−1 α U r−1 U2 ∗ −2 1 2/3 ) µα ≤ Cµ−2 α ≤ C(log 2∗ ,µ−1 α 2∗ ,µ−1 α = U 2∗ ,µ−1 α ≤ C(log We know |Yg (ξxg˜α ,λα ) − K −2 | ≤ Cµ4α log 1 2/3 ) . µα 1 . 1 we have uα Lr¯ (Bα ) ≥ C −1 µ2α log 1 µα 2/3 . Inserting into (64), we obtain αµ4α log 1 µα 4/3 ≤ C µ4α log 1 µα 4/3 + αµ4α log 1 . µα Once again we obtain α ≤ C, a contradiction. 1 is thus established in the remaining limit case n = 6. 2. We adapt some ideas from [6]. Let (M, g) be a smooth compact Riemannian manifold without boundary, n ≥ 3.

Lieb, One-electron relativistic molecules with Coulomb interaction, Comm. Math. Phys. 90 (1983), 497–510. [16] W. Ding, J. Jost, J. Li and G. Wang, The differential equation ∆u = 8π − 8πeu on a compact Riemannian surface, Asian J. Math. 1 (1997), 230–248. [17] O. Druet, The best constants problem in Sobolev inequalities, Math. Ann. 314 (1999), 327–346. [18] O. Druet, Isoperimetric inequalities on compact manifolds, Geometria Dedicata, to appear. [19] O. Druet, E. Hebey and M. Vaugon, Sharp Sobolev inequalities with lower order remainder terms, Trans.

Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), 479–495. [37] R. -T. Yau, Lectures on Differential Geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, Volume I, International Press, Boston, 1994. 34 [38] G. Stampacchia, Le probl`eme de Dirichlet pour les ´equations elliptiques du second ordre ` a coefficients discontinus, Ann. Inst. Fourier, Grenoble 15 (1965), 189–258. [39] M. Struwe, Critical points of embeddings of H01,n into Orlicz spaces, Ann.