All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 42 Next

Displaying 821 – 840 of 4028

Showing per page

Denseness and Borel complexity of some sets of vector measures

Zbigniew Lipecki (2004)

Studia Mathematica

Let ν be a positive measure on a σ-algebra Σ of subsets of some set and let X be a Banach space. Denote by ca(Σ,X) the Banach space of X-valued measures on Σ, equipped with the uniform norm, and by ca(Σ,ν,X) its closed subspace consisting of those measures which vanish at every ν-null set. We are concerned with the subsets ν ( X ) and ν ( X ) of ca(Σ,X) defined by the conditions |φ| = ν and |φ| ≥ ν, respectively, where |φ| stands for the variation of φ ∈ ca(Σ,X). We establish necessary and sufficient conditions...

Density of smooth maps for fractional Sobolev spaces W s , p into ℓ simply connected manifolds when s ≥ 1

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen (2013)

Confluentes Mathematici

Given a compact manifold N n ⊂ ℝ ν and real numbers s ≥ 1 and 1 ≤ p < ∞ , we prove that the class C ∞ ( Q ¯ m ; N n ) of smooth maps on the cube with values into N n is strongly dense in the fractional Sobolev space W s , p ( Q m ; N n ) when N n is ⌊ s p ⌋ simply connected. For s p integer, we prove weak sequential density of C ∞ ( Q ¯ m ; N n ) when N n is s p - 1 simply connected. The proofs are based on the existence of a retraction of ℝ ν onto N n except for a small subset of N n and on a pointwise estimate of fractional derivatives of composition of maps in W s , p ∩ W 1 , s p .

Denting point in the space of operator-valued continuous maps.

Ryszard Grzaslewicz, Samir B. Hadid (1996)

Revista Matemática de la Universidad Complutense de Madrid

In a former paper we describe the geometric properties of the space of continuous functions with values in the space of operators acting on a Hilbert space. In particular we show that dent B(L(H)) = ext B(L(H)) if dim H < 8 and card K < 8 and dent B(L(H)) = 0 if dim H < 8 or card K = 8, and x-ext C(K,L(H)) = ext C(K,L(H)).

Description of the lack of compactness for the Sobolev imbedding

P. Gérard (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove that any bounded sequence in a Hilbert homogeneous Sobolev space has a subsequence which can be decomposed as an almost-orthogonal sum of a sequence going strongly to zero in the corresponding Lebesgue space, and of a superposition of terms obtained from fixed profiles by applying sequences of translations and dilations. This decomposition contains in particular the various versions of the concentration-compactness principle.

Description of the lack of compactness of some critical Sobolev embedding

Hajer Bahouri (2011)

Journées Équations aux dérivées partielles

In this text, we present two recent results on the characterization of the lack of compactness of some critical Sobolev embedding. The first one derived in [5] deals with an abstract framework including Sobolev, Besov, Triebel-Lizorkin, Lorentz, Hölder and BMO spaces. The second one established in [3] concerns the lack of compactness of H 1 ( ℝ 2 ) into the Orlicz space. Although the two results are expressed in the same manner (by means of defect measures) and rely on the defect of compactness due to concentration...

Currently displaying 821 – 840 of 4028