共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Angelo Favini Gisèle Ruiz Goldstein Jerome A. Goldstein Enrico Obrecht Silvia Romanelli 《Mathematische Nachrichten》2010,283(4):504-521
We prove a very general form of the Angle Concavity Theorem, which says that if (T (t)) defines a one parameter semigroup acting over various Lp spaces (over a fixed measure space), which is analytic in a sector of opening angle θp, then the maximal choice for θp is a concave function of 1 – 1/p. This and related results are applied to give improved estimates on the optimal Lp angle of ellipticity for a parabolic equation of the form ?u /?t = Au, where A is a uniformly elliptic second order partial differential operator with Wentzell or dynamic boundary conditions. Similar results are obtained for the higher order equation ?u /?t = (–1)m +lAmu, for all positive integers m. 相似文献
3.
Wang Baoxiang 《数学学报(英文版)》1998,14(3):327-340
In this paper, we shall introduce the concept of the Bessel (Riesz) potential Köthe function spacesX s (X s ) and give some dual estimates for a class of operators determined by a semi-group in the spacesL q (?T, T; X s ) (L q (?T, T; X s )). Moreover, some time-spaceL p ?L p′ estimates for the semi-group exp(it(-Δ) m/2) and the operatorA:=∫ 0 t exp(i(t-τ)(-Δ) m/2)·dτ in the Lebesgue-Besov spacesL q (?T,T;B p,2 s are given. On the basis of these results, in a subsequent paper we shall present some further applications to a class of nonlinear wave equations. 相似文献
4.
We prove analogues of P. L. Ul’yanov and V. A. Andrienko results concerning embeddings of Lq Hölder spaces into Lebesgue spaces Lr or Lr Hölder spaces in the case 1 ≤ q < r ≤ 2 for functions defined on p-adic linear spaces. The conditions presented in these theorems are sharp. Also we give necessary and sufficient conditions for such embeddings in the case 1 ≤ q < r < ∞ that generalize recent results of S. S. Platonov.
相似文献5.
We use operator-valued Fourier multiplier theorems to study second order differential equations in Banach spaces. We establish
maximal regularity results in Lp and Cs for strong solutions of a complete second order equation.
In the second part, we study mild solutions for the second order problem. Two types of mild solutions are considered. When
the operator A involved is the generator of a strongly continuous cosine function, we give characterizations in terms of Fourier multipliers
and spectral properties of the cosine function. The results obtained are applied to elliptic partial differential operators.
The first author is supported in part by Convenio de Cooperación Internacional (CONICYT) Grant # 7010675 and the second author
is partially financed by FONDECYT Grant # 1010675 相似文献
6.
Jarosław Łazuka 《Mathematical Methods in the Applied Sciences》2020,43(17):10115-10137
This paper is devoted to the investigation of the solution to the Cauchy problem for a system of partial differential equations describing thermoelasticity of nonsimple materials in a three-dimensional space. The model of linear dynamical thermoelasticity of nonsimple materials is considered as the system of partial differential equations of fourth order. In this paper, we proposed a convenient evolutionary method of approach to the system of equations of nonsimple thermoelasticity. We proved the Lp−Lq time decay estimates for the solution to the Cauchy problem for linear thermoelasticity of nonsimple materials. 相似文献
7.
In this note we give a simple method to transfer the effect of the surface to the radial function in the kernel of singular
integral along surface. Using this idea, we give some continuity of the singular integrals along surface with Hardy space
function kernels on some function spaces, such as
Lp(\mathbb Rn),Lp(\mathbb Rn,w){L^p({\mathbb R}^n),L^p({\mathbb R}^n,\omega)}, Triebel–Lizorkin spaces
[(F)\dot]ps,q(\mathbb Rn){{\dot F}_{p}^{s,q}({\mathbb R}^n)}, Besov spaces
[(B)\dot]ps,q(\mathbb Rn){{\dot B}_{p}^{s,q}({\mathbb R}^n)}, generalized Morrey spaces
Lp,f(\mathbb Rn){L^{p,\phi}({\mathbb R}^n)} and Herz spaces
[(K)\dot]pa, q(\mathbb Rn){\dot K_p^{\alpha, q}({\mathbb R}^n)}. Our results improve and extend substantially some known results on the singular integral operators along surface. 相似文献
8.
In 1934, Whitney raised the question of how to recognize whether a function f defined on a closed subset X of ℝ
n
is the restriction of a function of class 𝒞
p
. A necessary and sufficient criterion was given in the case n=1 by Whitney, using limits of finite differences, and in the case p=1 by Glaeser (1958), using limits of secants. We introduce a necessary geometric criterion, for general n and p, involving limits of finite differences, that we conjecture is sufficient at least if X has a “tame topology”. We prove that, if X is a compact subanalytic set, then there exists q=q
X
(p) such that the criterion of order q implies that f is 𝒞
p
. The result gives a new approach to higher-order tangent bundles (or bundles of differential operators) on singular spaces.
Oblatum 21-XI-2001 & 3-VII-2002?Published online: 8 November 2002
RID="*"
ID="*"Research partially supported by the following grants: E.B. – NSERC OGP0009070, P.M. – NSERC OGP0008949 and the Killam
Foundation, W.P. – KBN 5 PO3A 005 21. 相似文献
9.
O. V. Besov 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):25-45
On an irregular domain G ⊂ ℝ
n
of a certain type, we introduce spaces of functions of fractional smoothness s > 0. We prove embedding theorems relating these spaces to the Sobolev spaces W
p
m
(G) and Lebesgue spaces L
p
(G). 相似文献
10.
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
11.
We prove a theorem about global existence (in time) of the solution to the initial‐value problem for a nonlinear hyperbolic parabolic system of coupled partial differential equation of second order describing the process of thermodiffusion in solid body. The corresponding global existence theorems has been proved using the Lp ‐ Lq time decay estimates for the solution of the associated linearized problem. Next, we proved the energy estimate in the Sobolev space with constant independent of time. Such an energy estimate allows us to apply the standard (continuation argument and to continue the local solution to one de.ned for all t ∈ 〈0, ∞)). 相似文献
12.
Romain Tessera 《Geometriae Dedicata》2008,136(1):203-220
We introduce a quantitative version of Property A in order to estimate the L
p
-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential volume growth. This quantitative property A also appears to
be useful to yield upper bounds on the L
p
-distortion of finite metric spaces. Namely, we obtain new optimal results for finite subsets of homogeneous Riemannian manifolds.
We also introduce a general form of Poincaré inequalities that provide constraints on compressions, and lower bounds on distortion.
These inequalities are used to prove the optimality of some of our results.
相似文献
13.
A. G. Baghdasaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(2):101-111
It is proved, that certain known function spaces (such as S
p,q
s
B, S
p,q
s
F spaces of functions of mixed smoothness and approximation spaces A
p,q
s
) can be characterized in terms of spaces of Sobolev-Liouville and Nikolskii-Besov type spaces and so called “B-products”. The representation theorems of S
p,q
s
B spaces are proved using B-products and covering method. It is proved that space S
p,q
s
B is a “real” method interpolation space for the pair of corresponding spaces of Nikolskii-Besov type. 相似文献
14.
In the first part of this paper, we discuss some properties of SΩ(Kn), L
P
Ω
(Kn) and L
P
Ω
(Kn;lq) spaces, give the Plancherel-Polya-Nikol’skij type inequalities and some multiplier theorems. In the second part of this
paper, using the results of Part I we prove some preliminary results for the spaces B
p,q
s
(Kn) and F
p,q
s
(Kn). 相似文献
15.
Eduardo Casas 《Numerical Functional Analysis & Optimization》2013,34(2):117-137
ABSTRACT For a polygonal open bounded subset of ?2, of boundary Γ, we study stability estimates for the projection operator from L 1(Γ) on a convex set K h of continuous piecewise affine functions satisfying bound constraints. We establish stability estimates in L p (Γ) and in W s,p (Γ) for 1 ≤ p ≤ ∞ and 0 < s ≤ 1. This kind of result plays a crucial role in error estimates for the numerical approximation of optimal control problems of partial differential equations with bilateral control constraints. 相似文献
16.
Enrico Giusti 《Annali di Matematica Pura ed Applicata》1967,75(1):313-353
Summary Regularity theorems inL
2, θ (ω, δ) spaces are proved for weak solutions of quasielliptic differential equations. In particular, regularization results
are obtained in the class of holder continuous functions (with respect to a suitable metric related to the operator). As a
consequence, we obtain results and estimates in Lp andL
p, θ spaces for the solution of the Dirichlet problem.
Lavoro eseguito nell’ambito del Gruppo di Ricerca no 46 del Comitato per la Matematica del C N.R. 相似文献
Lavoro eseguito nell’ambito del Gruppo di Ricerca no 46 del Comitato per la Matematica del C N.R. 相似文献
17.
A. S. Fedorenko 《Ukrainian Mathematical Journal》1999,51(12):1945-1949
We obtain estimates exact in order for the best trigonometric and orthogonal trigonometric approximations of the classesL Ψβ,ρ of functions of one variable in the spaceL q in the case 2<p <q < ∞. 相似文献
18.
Let X be a Banach space. We show that each m : ? \ {0} → L (X ) satisfying the Mikhlin condition supx ≠0(‖m (x )‖ + ‖xm ′(x )‖) < ∞ defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is isomorphic to a Hilbert space; each bounded measurable function m : ? → L (X ) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is a UMD space. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
O. V. Besov 《Proceedings of the Steklov Institute of Mathematics》2008,260(1):25-36
On an irregular domain G ⊂ ℝ
n
of a certain type, we introduce function spaces of fractional smoothness s > 0 that are similar to the Lizorkin-Triebel spaces. We prove embedding theorems that show how these spaces are related to
the Sobolev and Lebesgue spaces W
p
m
(G) and L
p
(G).
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 260, pp. 32–43. 相似文献
20.
V. N. Konovalov 《Ukrainian Mathematical Journal》2005,57(12):1911-1936
Let s ∈ ℕ and let Δ
+
s
be the set of functions x: I ↦ ℝ on a finite interval I such that the divided differences [x; t
0, ..., t
s
] of order s of these functions are nonnegative for all collections of s + 1 different points t
0, ..., t
s
∈ I. For the classes Δ
+
s
B
p
: = Δ
+
s
∩ B
p
, where B
p
is the unit ball in L
p
, we determine the orders of Kolmogorov and linear widths in the spaces Lq
for 1 ≤ q > p ≤ ∞.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1633–1652, December, 2005. 相似文献