共查询到20条相似文献,搜索用时 11 毫秒
1.
We derive interior L
p
-estimates for solutions of linear elliptic systems with oscillatory coefficients. The estimates are independent of ε, the small length scale of the rapid oscillations. So far, such results are based on potential theory and restricted to periodic
coefficients. Our approach relies on BMO-estimates and an interpolation argument, gradients are treated with the help of finite
differences. This allows to treat coefficients that depend on a fast and a slow variable. The estimates imply an L
p
-corrector result for approximate solutions.
相似文献
2.
Kyeong-Hun Kim 《Potential Analysis》2008,29(3):303-326
Stochastic partial differential equations are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular, it can be negative and fractional. It is allowed that the coefficients of the equations blow up near the boundary. 相似文献
3.
Stochastic partial differential equations of divergence form are considered in C1 domains. Existence and uniqueness results are given in a Sobolev space with weights allowing the derivatives of the solutions to blow up near the boundary.Mathematics Subject Classification (2000): 60H15, 35R60 相似文献
4.
The paper investigates L
p
convergence and Marcinkiewicz-Zygmund strong laws of large numbers for random elements in a Banach space under the condition
that the Banach space is of Rademacher type p, 1 < p < 2. The paper also discusses L
r
convergence and L
r
bound for random elements without any geometric restriction condition on the Banach space. 相似文献
5.
L. Olsen 《Monatshefte für Mathematik》2005,146(2):143-157
For a probability measure μ on a subset of
, the lower and upper Lq-dimensions of order
are defined by
We study the typical behaviour (in the sense of Baire’s category) of the Lq-dimensions
and
. We prove that a typical measure μ is as irregular as possible: for all q ≥ 1, the lower Lq-dimension
attains the smallest possible value and the upper Lq-dimension
attains the largest possible value. 相似文献
6.
Xiang-Dong Li 《Journal of Geometric Analysis》2010,20(2):354-387
We prove some Sobolev inequalities on differential forms over a class of complete non-compact Riemannian manifolds with suitable
geometric conditions. Moreover, we establish some L
p,q
-estimates and existence theorems of the Cartan-De Rham equation and the Hodge systems. As applications, we prove some vanishing
theorems of the L
p,q
-cohomology and prove the L
q
-solvability of the nonlinear p-Laplace equation on forms on complete non-compact Riemannian manifolds with suitable geometric conditions. 相似文献
7.
A. I. Kamzolov 《Moscow University Mathematics Bulletin》2007,62(4):158-162
Asymptotic estimates of L q -norms of partial sums of Fourier-Legendre series of functions from L p [?1; 1] are obtained. 相似文献
8.
A weighted norm inequality for the Marcinkiewicz integral operator
is proved when belongs to
. We also give the weighted
Lp-boundedness for a class of Marcinkiewicz integral operators with rough
kernels
and
related to the Littlewood-Paley
-function and the
area integral S, respectively. 相似文献
9.
Let G be a locally compact group, ω be a weight function on G and 1 < p < ∞. Here, we give a sufficient condition for that the weighted L
p
-space L
p
(G, ω) is a Banach algebra. Also, we get some necessary conditions on G and the weight function ω for L
p
(G, ω) to be a Banach algebra. As a consequence, we show that if G is abelian and L
p
(G, ω) is a Banach algebra, then G is σ-compact. 相似文献
10.
In this paper, the Lp(Rn)-boundedness of the commutators generalized by BMO(Rn) function and the singular integral operator T with rough kernel Ω∈ Llog+ L(Sn-1) is proved by using the Bony's formula for the paraproduct of two functions. 相似文献
11.
Octavian G. Mustafa 《Annali di Matematica Pura ed Applicata》2008,187(2):187-196
Via an integral transformation, we establish two embedding results between the Emden-Fowler type equation , t ≥ t
0 > 0, with solutions x such that as , , and the equation , u > 0, with solutions y such that for given k > 0. The conclusions of our investigation are used to derive conditions for the existence of radial solutions to the elliptic
equation , , that blow up as in the two dimensional case.
相似文献
12.
For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by
where = (y
1,y
2, ···, y
m
) and denotes the m-tuple (f
1,f
2, ···, f
m
). In this note, the one-weighted and two-weighted boundedness on L
p
(ℝ
n
) space for multilinear fractional integral operator I
α(m) and the fractional multi-sublinear maximal operator M
α(m) are established respectively. The authors also obtain two-weighted weak type estimate for the operator M
α(m).
Supported in Part by the NNSF of China under Grant #10771110, and by NSF of Ningbo City under Grant #2006A610090. 相似文献
13.
We consider the operator ${\cal A}$ formally defined by ${\cal
A}u(x)=\alpha(x)\Delta u(x)$
for any $x$ in a sufficiently smooth bounded open set
$\Om\subset\R^N$ ($N\ge 1$), where $\alpha\in C(\ov\Omega)$ is a
continuous nonnegative function vanishing only on $\partial\Omega$,
and such that $1/\alpha$ is integrable in $\Omega$.
We prove that the realization $A_p$ of ${\cal A}$, equipped with
suitable nonlinear boundary conditions is an m-dissipative operator in
suitably weighted $L^p(\Omega)$-spaces in the
case where either $(p,N)\in (1,+\infty)\times\{1\}$ or
$(p,N)=\{2\}\times\N$. Moreover, we prove that $A_p$ is a densely
defined closed operator.
We consider nonlinear boundary conditions of the following type: in the one
dimensional case we take $\Omega=(0,1)$ and we assume that
$u(j)=(-1)^j\beta_j(u(j))$ ($j=0,1$), $\beta_0$ and $\beta_1$ being
nondecreasing continuous functions in $\R$ such that
$\beta_0(0)=\beta_1(0)=0$; in the $N$-dimensional setting we
assume that
$(D_{\nu}u)_{|\partial\Omega}=-\beta(u_{|\partial\Omega})$, $\beta$
being a nondecreasing Lipschitz continuous function in $\R$ such that
$\beta(0)=0$. Here $\nu$ denotes the unit outward normal to
$\partial\Om$. 相似文献
14.
The order components of a finite group are introduced in [12]. In [9], it is proved that the group PSL(3,q), where q is an odd prime power, is uniquely determined by its order components. In this paper, we show that the group PSL(3, q), where q=2
m
, is also uniquely determined by its order components.
Received December 15, 2000, Revised August 15, 2001, Accepted November 13, 2001 相似文献
15.
In this paper we obtain local L
p
estimates for the parabolic polyharmonic equations by a straightforward approach.
Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic
Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported
by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant
No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017) 相似文献
16.
From a one-point iterative method of R-order at least three, we construct new two-point iterations to solve nonlinear equations in Banach spaces such that the computational
cost is reduced, whereas the R-order of convergence is increased to at least four.
相似文献
17.
An existence result for a strongly non-linear elliptic equation with natural growth condition on the non-linearity and L1-data is proved. Mathematics Subject Classification (2000) 35J25, 35J60 相似文献
18.
We investigate R-bounded representations
, where X is a Banach space and G is a lca group. Observing that Ψ induces a (strongly continuous) group homomorphism
, we are then able to analyze certain classical homomorphisms U (e.g. translations in Lp (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.
Dedicated to the memory of H. H. Schaefer 相似文献
19.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献
20.
We give a characterization of structurally stable diffeomorphisms by making use of the notion of L
p
-shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C
1-interior of the set of diffeomorphisms having L
p
-shadowing property. 相似文献