The nonlinear Neumann problem and sharp weighted Sobolev inequalities
نویسندگان
چکیده
منابع مشابه
SHARP AFFINE Lp SOBOLEV INEQUALITIES
In this paper we prove a sharp affine Lp Sobolev inequality for functions on R. The new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin [A2] and Talenti [T], even though it uses only the vector space structure and standard Lebesgue measure on R. For the new inequality, no inner product, norm, or conformal structure is needed at...
متن کاملSharp Sobolev inequalities involving boundary terms
Let (M, g) be a compact Riemannian manifold of dimension n (n ≥ 3) with smooth boundary. In [LZ], we established some sharp trace inequality on (M, g). In this paper we establish some sharp Sobolev inequalities using the method in [LZ]. For n ≥ 3, it was shown by Aubin [Au1] and Talenti [T] that, for p = 2n/(n − 2), 1 S 1 = inf R n |∇u| 2 R n |u| p 2/p u ∈ L p (R n) \ {0}, ∇u ∈ L 2 (R n) , (0.1...
متن کاملThe ∂-neumann Problem in the Sobolev Topology
Here, and throughout the paper, we useD to denote the α-order derivative, where α is a multi-index and we are using standard multi-index notation. Moreover, γα := |α|!/α! denotes the polynomial coefficient. [The naturality of this choice of the Sobolev inner product will be pointed out and discussed below.] We define the Sobolev space W (Ω) to be the closure of C(Ω̄) with respect to the above in...
متن کاملSome general forms of sharp Sobolev inequalities
In this paper, we establish some general forms of sharp Sobolev inequalities on the upper half space or any compact Riemannian manifold with smooth boundary. These forms extend some previous results due to Escobar [11], Li and Zhu [18].
متن کاملA Hierarchical Structure for the Sharp Constants of Discrete Sobolev Inequalities on a Weighted Complete Graph
This paper clarifies the hierarchical structure of the sharp constants for the discrete Sobolev inequality on a weighted complete graph. To this end, we introduce a generalized-graph Laplacian A = I − B on the graph, and investigate two types of discrete Sobolev inequalities. The sharp constants C0(N; a) and C0(N) were calculated through the Green matrix G(a) = (A + aI)−1(0 < a < ∞) and the pse...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2001
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm88-2-3