共查询到20条相似文献,搜索用时 15 毫秒
1.
Let Θ be a bounded open set in ℝ
n
, n ⩾ 2. In a well-known paper Indiana Univ. Math. J., 20, 1077–1092 (1971) Moser found the smallest value of K such that
$
\sup \left\{ {\int_\Omega {\exp \left( {\left( {\frac{{\left| {f(x)} \right|}}
{K}} \right)^{{n \mathord{\left/
{\vphantom {n {(n - 1)}}} \right.
\kern-\nulldelimiterspace} {(n - 1)}}} } \right):f \in W_0^{1,n} (\Omega ),\left\| {\nabla f} \right\|_{L^n } \leqslant 1} } \right\} < \infty
$
\sup \left\{ {\int_\Omega {\exp \left( {\left( {\frac{{\left| {f(x)} \right|}}
{K}} \right)^{{n \mathord{\left/
{\vphantom {n {(n - 1)}}} \right.
\kern-\nulldelimiterspace} {(n - 1)}}} } \right):f \in W_0^{1,n} (\Omega ),\left\| {\nabla f} \right\|_{L^n } \leqslant 1} } \right\} < \infty
相似文献
2.
Vladimir I. Ovchinnikov 《Journal of Functional Analysis》2005,228(1):234-243
We consider a generalization ?(X0,X1)p0,p1 of the method of means to arbitrary non-degenerate functional parameter. In this case non-trivial embedding ?(X0,X1)p0,p1⊂ψ(X0,X1)q0,q1 take place. We find necessary and sufficient condition for such embedding if 1?q0?p0?∞ and 1?q1?p1?∞ or 1?p0?q0?∞ and 1?p1?q1?∞. 相似文献
3.
We study Sobolev embedding theorems in Lorentz-Zygmund spaces. Some limiting cases are considered.Supported by M.U.R.S.T. (1990). 相似文献
4.
We compute the limits of higher-order Besov norms and derive the sharp constants for certain forms of the Sobolev embedding theorem. Our results extend to higher-order spaces the recent work by Brézis-Bourgain-Mironescu and Maz’ya-Shaposhnikova. The interpolation methods we develop are of interest on their own and could have applications to related inequalities. 相似文献
5.
We exhibit balance conditions between a Young function A and a Young function B for a Korn type inequality to hold between the LB norm of the gradient of vector-valued functions and the LA norm of its symmetric part. In particular, we extend a standard form of the Korn inequality in Lp, with 1<p<∞, and an Orlicz version involving a Young function A satisfying both the Δ2 and the ∇2 condition. 相似文献
6.
We prove a refined limiting imbedding theorem of the Brézis-Wainger type in the first critical case, i.e. , for Sobolev spaces and Bessel potential spaces of functions with values in a general Banach space E. In particular, the space E may lack the UMD property. 相似文献
7.
In this paper, we have established some compact imbedding theorems for some subspaces of W1,p(x)(U) when the underlying domain U is unbounded. The domain we consider is mainly of type RN(N≥2) or RL×Ω(L≥2), where Ω⊂RM is a bounded domain with smooth boundary. 相似文献
8.
9.
Serguei V. Astashkin 《Journal of Functional Analysis》2005,226(1):173-192
Let X be a rearrangement invariant (r.i.) function space on [0,1]. We consider the Rademacher multiplicator space Λ(R,X) of measurable functions x such that xh∈X for every a.e. converging series h=∑anrn∈X, where (rn) are the Rademacher functions. We show that for a broad class of r.i. spaces X, the space Λ(R,X) is not r.i. In this case, we identify the symmetric kernel of the Rademacher multiplicator space and study when reduces to L∞. In the opposite direction, we find new examples of r.i. spaces for which Λ(R,X) is r.i. We consider in detail the case when X is a Marcinkiewicz or an exponential Orlicz space. 相似文献
10.
11.
12.
13.
A class of bounded operators on Sobolev spaces 总被引:2,自引:0,他引:2
We describe a class of nonlinear operators which are bounded on the
Sobolev spaces
, for
and 1 < p <
. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on
, for
and 1 < p <
; this extends the result of J. Kinnunen [7], valid for s = 1.
Received: 5 December 2000 相似文献
14.
The aim of this article is to characterize compactly supported refinable distributions in Triebel-Lizorkin spaces and Besov spaces by projection operators on certain wavelet space and by some operators on a finitely dimensional space.Research partially supported by the National Natural Sciences Foundation of China # 69735020, the Tian Yuan Projection of the National Natural Sciences Foundation of China, the Doctoral Bases Promotion Foundation of National Educational Commission of China #97033519 and the Zhejiang Provincial Sciences Foundation of China # 196083, and by the Wavelets Strategic Research Program funded by the National Science and Technology Board and the Ministry of Education, Singapore. 相似文献
15.
Aneta Wróblewska 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):4136-2679
Our purpose is to show the existence of weak solutions to steady flow of non-Newtonian incompressible fluids with nonstandard growth conditions of the Cauchy stress tensor. We are motivated by the fluids of strongly inhomogeneous behavior and characterized by rapid shear thickening. Since Lp framework is not sufficient to capture the described model, we describe the growth conditions with the help of a general x-dependent convex function and formulate our problem in generalized Orlicz spaces. 相似文献
16.
Oscar Domínguez 《Mathematische Nachrichten》2016,289(14-15):1739-1759
This paper deals with dimension‐controllable (tractable) embeddings of Besov spaces on n‐dimensional torus into small Lebesgue spaces. Our techniques rely on the approximation structure of Besov spaces, extrapolation properties of small Lebesgue spaces and interpolation. 相似文献
17.
Xianling Fan 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):4148-4161
The classical Morrey spaces and Campanato spaces are generalized to the variable exponent case. The definitions and some basic properties of the variable exponent Morrey and Campanato spaces are presented. A concept of the p(⋅)-average of the functions is introduced. 相似文献
18.
Sun-Sig Byun 《Journal of Differential Equations》2009,246(9):3518-3327
We establish the global Hessian estimate in Orlicz spaces for a fourth-order parabolic system with discontinuous tensor coefficients in a non-smooth domain under the assumptions that the coefficients have small weak BMO semi-norms, the boundary of a domain is δ-Reifenberg flat for δ>0 small and the given Young function satisfies some moderate growth condition. As a corollary we obtain an optimal global W2,p regularity for such a system. 相似文献
19.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
20.
Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev type inequalities of any order, involving arbitrary rearrangement-invariant norms, on open sets in Rn, possibly endowed with a measure density, are reduced to much simpler one-dimensional inequalities for suitable integral operators depending on the isoperimetric function of the relevant sets. As a consequence, the optimal target space in the relevant Sobolev embeddings can be determined both in standard and in non-standard classes of function spaces and underlying measure spaces. In particular, our results are applied to any-order Sobolev embeddings in regular (John) domains of the Euclidean space, in Maz'ya classes of (possibly irregular) Euclidean domains described in terms of their isoperimetric function, and in families of product probability spaces, of which the Gauss space is a classical instance. 相似文献
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