共查询到20条相似文献,搜索用时 31 毫秒
1.
It is proved that if Ω ⊂ Rn {R^n} is a bounded Lipschitz domain, then the inequality
|| u ||1 \leqslant c(n)\textdiam( W)òW | eD(u) | {\left\| u \right\|_1} \leqslant c(n){\text{diam}}\left( \Omega \right)\int\limits_\Omega {\left| {{\varepsilon^D}(u)} \right|} is valid for functions of bounded deformation vanishing on ∂Ω. Here eD(u) {\varepsilon^D}(u) denotes the deviatoric part of the symmetric gradient and òW | eD(u) | \int\limits_\Omega {\left| {{\varepsilon^D}(u)} \right|} stands for the total variation of the tensor-valued measure eD(u) {\varepsilon^D}(u) . Further results concern possible extensions of this Poincaré-type inequality. Bibliography: 27 titles. 相似文献
2.
LetR
n be n-dimensional Euclidean space with n>-3. Demote by Ω
n
the unit sphere inR
n. ForfɛL(Ω
n
) we denote by σ
N
δ
its Cesàro means of order σ for spherical harmonic expansions. The special value
l = \tfracn - 22\lambda = \tfrac{{n - 2}}{2}
of σ is known as the critical one. For 0<σ≤λ, we set
p0 = \tfrac2ld+ lp_0 = \tfrac{{2\lambda }}{{\delta + \lambda }}
.
This paper proves that
limN ? ¥ || sNd (f) - f ||p0 = 0\mathop {\lim }\limits_{N \to \infty } \left\| {\sigma _N^\delta (f) - f} \right\|p_0 = 0 相似文献
3.
Let Ω ⊂ ℝ
d
be a compact convex set of positive measure. In a recent paper, we established a definiteness theory for cubature formulae
of order two on Ω. Here we study extremal properties of those positive definite formulae that can be generated by a centroidal
Voronoi tessellation of Ω. In this connection we come across a class of operators of the form Ln[f](x): = ?i=1n fi(x)(f(yi) + á?f(yi), x-yi?)L_n[f](\boldsymbol{x}):= \sum_{i=1}^n \phi_i(\boldsymbol{x})(f(\boldsymbol{y}_i) + \langle\nabla f(\boldsymbol{y}_i), \boldsymbol{x}-\boldsymbol{y}_i\rangle), where y1,..., yn\boldsymbol{y}_1,\dots, \boldsymbol{y}_n are distinct points in Ω and {ϕ
1, ..., ϕ
n
} is a partition of unity on Ω. We present best possible pointwise error estimates and describe operators L
n
with a smallest constant in an L
p
error estimate for 1 ≤ p < ∞ . For a generalization, we introduce a new type of Voronoi tessellation in terms of a twice continuously differentiable
and strictly convex function f. It allows us to describe a best operator L
n
for approximating f by L
n
[f] with respect to the L
p
norm. 相似文献
4.
Reinhard Farwig Christian Komo 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):303-321
Let u be a weak solution of the Navier–Stokes equations in an exterior domain ${\Omega \subset \mathbb{R}^3}
5.
In this paper, we will establish some new properties of traveling waves for integrodifference equations with the nonmonotone
growth functions. More precisely, for c ≥ c
*, we show that either limx?+¥ f(x)=u*{\lim\limits_{\xi\rightarrow+\infty} \phi(\xi)=u*} or 0 < liminfx? + ¥ f(x) < u* < limsupx?+¥f(x) £ b,{0 < \liminf\limits_{\xi \rightarrow + \infty} \phi(\xi) < u* < \limsup \limits_{\xi\rightarrow+\infty}\phi(\xi)\leq b,} that is, the wave converges to the positive equilibrium or oscillates about it at +∞. Sufficient conditions can assure that
both results will arise. We can also obtain that any traveling wave with wave speed c > c* possesses exponential decay at −∞. These results can be well applied to three types of growth functions arising from population
biology. By choosing suitable parameter numbers, we can obtain the existence of oscillating waves. Our analytic results are
consistent with some numerical simulations in Kot (J Math Biol 30:413–436, 1992), Li et al. (J Math Biol 58:323–338, 2009) and complement some known ones. 相似文献
6.
Let
W í \Bbb C\Omega \subseteq {\Bbb C}
be a simply connected domain in
\Bbb C{\Bbb C}
, such that
{¥} è[ \Bbb C \[`(W)]]\{\infty\} \cup [ {\Bbb C} \setminus \bar{\Omega}]
is connected. If g is holomorphic in Ω and every derivative of g extends continuously on
[`(W)]\bar{\Omega}
, then we write g ∈ A∞ (Ω). For g ∈ A∞ (Ω) and
z ? [`(W)]\zeta \in \bar{\Omega}
we denote
SN (g,z)(z) = ?Nl=0\fracg(l) (z)l ! (z-z)lS_N (g,\zeta )(z)= \sum^{N}_{l=0}\frac{g^{(l)} (\zeta )}{l !} (z-\zeta )^l
. We prove the existence of a function f ∈ A∞(Ω), such that the following hold:
7.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
\Bbb C{\Bbb C}
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
Cn(W,P) := supf ? A(W,P)supz ? W\frac|f(n)(z)| R(f(z),P)n! (R(z,W))nC_n(\Omega,\Pi)\,:=\,\sup_{f\in A(\Omega,\Pi)}\sup_{z\in \Omega}\frac{\vert f^{(n)}(z)\vert\,R(f(z),\Pi)}{n!\,(R(z,\Omega))^n}
are finite for all
n ? \Bbb N{n \in {\Bbb N}}
if and only if ∂Ω and ∂Π do not contain isolated points. 相似文献
8.
We show that any entropy solution u of a convection diffusion equation ?t u + div F(u)-Df(u) = b{\partial_t u + {\rm div} F(u)-\Delta\phi(u) =b} in Ω × (0, T) belongs to C([0,T),L1loc(W)){C([0,T),L^1_{\rm loc}({\Omega}))} . The proof does not use the uniqueness of the solution. 相似文献
9.
Inspired by the work of Marcellini and Papi, we consider local minima u: ℝ
n
⊃ Ω → ℝ
M
of variational integrals òW h( | ?u | ) \int\limits_\Omega {h\left( {\left| {\nabla u} \right|} \right)} dx and prove interior gradient bounds under rather general assumptions on h provided that u is locally bounded. Our requirements on the density h do not involve the dimension n. Bibliography: 18 titles. 相似文献
10.
Sylvain Roy 《Arkiv f?r Matematik》2008,46(1):153-182
Let Ω be an open subset of R
d
, d≥2, and let x∈Ω. A Jensen measure for x on Ω is a Borel probability measure μ, supported on a compact subset of Ω, such that ∫u
dμ≤u(x) for every superharmonic function u on Ω. Denote by J
x
(Ω) the family of Jensen measures for x on Ω. We present two characterizations of ext(J
x
(Ω)), the set of extreme elements of J
x
(Ω). The first is in terms of finely harmonic measures, and the second as limits of harmonic measures on decreasing sequences
of domains.
This allows us to relax the local boundedness condition in a previous result of B. Cole and T. Ransford, Jensen measures and
harmonic measures, J. Reine Angew. Math.
541 (2001), 29–53.
As an application, we give an improvement of a result by Khabibullin on the question of whether, given a complex sequence
{α
n
}
n=1
∞ and a continuous function , there exists an entire function f≢0 satisfying f(α
n
)=0 for all n, and |f(z)|≤M(z) for all z∈C. 相似文献
11.
V. V. Zhuk 《Journal of Mathematical Sciences》2010,166(2):167-185
Let L
p
, 1 ≤ p< ∞, be the space of 2π-periodic functions f with the norm
|| f ||p = ( ò - pp | f |p )1 \mathord | / |
\vphantom 1 p p {\left\| f \right\|_p} = {\left( {\int\limits_{ - \pi }^\pi {{{\left| f \right|}^p}} } \right)^{{1 \mathord{\left/{\vphantom {1 p}} \right.} p}}} , and let C = L
∞ be the space of continuous 2π-periodic functions with the norm
|| f ||¥ = || f || = maxe ? \mathbbR | f(x) | {\left\| f \right\|_\infty } = \left\| f \right\| = \mathop {\max }\limits_{e \in \mathbb{R}} \left| {f(x)} \right| . Let CP be the subspace of C with a seminorm P invariant with respect to translation and such that
P(f) \leqslant M|| f || P(f) \leqslant M\left\| f \right\| for every f ∈ C. By ?k = 0¥ Ak (f) \sum\limits_{k = 0}^\infty {{A_k}} (f) denote the Fourier series of the function f, and let l = { lk }k = 0¥ \lambda = \left\{ {{\lambda_k}} \right\}_{k = 0}^\infty be a sequence of real numbers for which ?k = 0¥ lk Ak(f) \sum\limits_{k = 0}^\infty {{\lambda_k}} {A_k}(f) is the Fourier series of a certain function f
λ ∈ L
p
. The paper considers questions related to approximating the function f
λ by its Fourier sums S
n
(f
λ) on a point set and in the spaces L
p
and CP. Estimates for || fl - Sn( fl ) ||p {\left\| {{f_\lambda } - {S_n}\left( {{f_\lambda }} \right)} \right\|_p} and P(f
λ − S
n
(f
λ)) are obtained by using the structural characteristics (the best approximations and the moduli of continuity) of the functions
f and f
λ. As a rule, the essential part of deviation is estimated with the use of the structural characteristics of the function f.
Bibliography: 11 titles. 相似文献
12.
Jorge García-Melián 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,31(2):594-607
In this paper we consider the boundary blow-up problem Δpu = a(x)uq in a smooth bounded domain Ω of
\mathbbRN{\mathbb{R}}^N, with u = +∞ on ∂Ω. Here Dpu = div(|?u|p-2?u)\Delta_{p}u = {\rm div}(|\nabla u|^{p-2}\nabla u) is the well-known p-Laplacian operator with p > 1, q > p − 1, and a(x) is a nonnegative weight function which can be singular on ∂Ω. Our results include existence, uniqueness and exact boundary
behavior of positive solutions. 相似文献
13.
A question of Yves Meyer motivated the research concerning “time” subordinations of real functions. Denote by B1a{\mathcal {B}}_{1}^{\alpha} the metric space of functions with Lipschitz constant 1 defined on [0,1], equipped with the complete metric defined via the
supremum norm. Given a function g ? B1ag\in {\mathcal {B}}_{1}^{\alpha} one obtains a time subordination of g simply by considering the composite function Z=g○f, where f∈ℳ:={f:f(0)=0, f(1)=1 and
f
is a continuous nondecreasing function on [0,1]}. The metric space Ea=M×B1a\mathcal {E}^{\alpha}=\mathcal {M}\times {\mathcal {B}}_{1}^{\alpha} equipped with the product supremum metric is a complete metric space. In this paper for all α∈[0,1) multifractal properties of g○f are investigated for a generic (typical) element (f,g)∈ℰ
α
. In particular we determine the generic H?lder singularity spectrum of g○f. 相似文献
14.
The aim of this study is to prove global existence of classical solutions for systems of the form ${\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)}
15.
Adimurthi João Marcos do Ó Kyril Tintarev 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(4):467-477
The paper studies quasilinear elliptic problems in the Sobolev spaces W 1,p (Ω), ${\Omega\subset{\mathbb R}^N}
16.
We survey recent results related to uniqueness problems for parabolic equations for measures. We consider equations of the
form ∂
t
μ = L
*
μ for bounded Borel measures on ℝ
d
× (0, T), where L is a second order elliptic operator, for example, Lu = Dxu + ( b,?xu ) Lu = {\Delta_x}u + \left( {b,{\nabla_x}u} \right) , and the equation is understood as the identity
|