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1.
We consider finite element methods applied to a class of Sobolev equations inR d(d ≥ 1). Global strong superconvergence, which only requires that partitions are quais-uniform, is investigated for the error between the approximate solution and the Ritz-Sobolev projection of the exact solution. Two order superconvergence results are demonstrated inW 1,p (Ω) andL p(Ω) for 2 ≤p < ∞.  相似文献   

2.
Let Ω be a bounded co.nvex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△ on Ω. Let hrp(Ω) = {f ∈ D'(Ω) :(E)F∈hp(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f→(△)2(Gf) for every f ∈ hrp(Ω) is obtained, where n/(n 1)<p≤1.  相似文献   

3.
In this paper, the spaceD p(Ω) of functions holomorphic on bounded symmetric domain ofC n is defined. We prove thatH p(Ω)⊂D p(Ω) if 0<p≤2, andD p(Ω)⊂H p(Ω) ifp≥2, and both the inclusions are proper. Further, we find that some theorems onH p(Ω) can be extended to a wider classD p(Ω) for 0<p≤2.  相似文献   

4.
Riassunto Nel cilindroQ=Ω×(0,T) si considerano sistemi parabolici (E+ϖ/ϖt) di forma non variazionale e con coefficienti discontinui, e si dimostra un teorema di isomorfismoW 0 p (Q)→L p (Q;R N ) e un teorema di regolarità locale negli spazi di Morrey.
Summary In the cylinderQ=Ω×(0, T) we consider parabolic systems (E+ϖ/ϖt), in non variational form and with discontinuous coefficients, and we prove an theorem of isomorphismW 0 p (Q)→L p (Q;R N ) and an theorem of local regularity in the Morrey’s spaces.


Lavoro eseguito nell’ambito del gruppo G.N.A.F.A. del C.N.R.  相似文献   

5.
Let Ω be an open and bounded subset ofR n with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R m ) whose jump setS vis essentially closed and polyhedral and which are of classW k, ∞ (S v,R m) for every integerk are strongly dense inGSBV p(Ω,R m ), in the sense that every functionu inGSBV p(Ω,R m ) is approximated inL p(Ω,R m ) by a sequence of functions {v k{j∈N with the described regularity such that the approximate gradients ∇v jconverge inL p(Ω,R nm ) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS v j converges to the (n−1)-dimensional measure ofS u. The structure ofS v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneuGSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.
  相似文献   

6.
Following our previous paper [LZ] which deals with the groupU(n, n), we study the structure of certain Howe quotients Ω p,q and Ω p,q (1) which are natural Sp(2n,R) modules arising from the Oscillator representation associated with the dual pair (O(p, q), Sp(2n,R)), by embedding them into the degenerate principal series representations of Sp(2n,R) studied in [L2].  相似文献   

7.
In this note, the regularity of Poisson equation -△u = f with f lying in logarithmic function space Lp(LogL)a(Ω)(1<p <∞, a ∈ R) is studied. The result of the note generalizes the W2,p estimate of Poisson equation in Lp(Ω).  相似文献   

8.
Let Ω⊂R n be an arbitrary open set. In this paper it is shown that if a Sobolev functionfW 1,p (Ω) possesses a zero trace (in the sense of Lebesgue points) on ϖΩ, thenf is weakly zero on ϖΩ in the sense thatfW 0 1,p (Ω).  相似文献   

9.
Letf be a non-decreasing C1-function such that andF(t)/f 2 a(t)→ 0 ast → ∞, whereF(t)=∫ 0 t f(s) ds anda ∈ (0, 2]. We prove the existence of positive large solutions to the equationΔu +q(x)|Δu| a =p(x)f(u) in a smooth bounded domain Ω ⊂RN, provided thatp, q are non-negative continuous functions so that any zero ofp is surrounded by a surface strictly included in Ω on whichp is positive. Under additional hypotheses onp we deduce the existence of solutions if Ω is unbounded.  相似文献   

10.
This paper is concerned with several approximation problems in the weighted Hardy spacesH p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH p(Ω) coincides, moduloH p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan sets forH p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH p(D), 1 ⪯p < ∞. Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday.  相似文献   

11.
Let ζ be a primitivesp-th root of unity for a primep>2, and consider the group Ω(ζ) of cyclotomic units in the ringR(ζ)=ℒ[ζ+ζ-1]. This paper deals with the image of Ω(ζ) in the unit group ofR(ζ)/qR(ζ), whereq is a prime ≠p. In particular, it obtains criteria for this image to be essentially everything, and a lower bound on the density of primesp (withq fixed) for which it cannot be. These results have a direct bearing on previous work about units in integral group rings for cyclic groups of orderpq. Work supported in part by an operating grant from NSERC (Canada).  相似文献   

12.
In this paper we investigate Riesz transforms R μ (k) of order k≥1 related to the Bessel operator Δμ f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every k≥1, R μ (k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x 2μ+1dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R μ (k) maps L p (ω) into itself and L 1(ω) into L 1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman.  相似文献   

13.
Summary Letf: (x, z)∈R n×Rn→f(x, z)∈[0, +∞] be measurable inx and convex inz. It is proved, by an example, that even iff verifies a condition as|z| p≤f(x, z)≤Λ(a(x)+|z|q) with 1<p<q,aL loc s (R n),s>1, the functional that isL 1(Ω)-lower semicontinuous onW 1,1(Ω), does not agree onW 1,1(Ω) with its relaxed functional in the topologyL 1(Ω) given by inf
Riassunto Siaf: (x, z)∈R n×Rn→f(x, z)∈[0, +∞] misurabile inx e convessa inz. Si mostra con un esempio che anche sef verifica una condizione del tipo|z| p≤f(x, z)≤Λ(a(x)+|z|q) con 1<p<q,aL loc s (R n),s>1, il funzionale , che èL 1(Ω)-semicontinuo inferiormente suW 1,1(Ω), non coincide suW 1,1(Ω) con il suo funzionale rilassato nella topologiaL 1(Ω) definito da inf
  相似文献   

14.
Summary In this paper we study, in the framework of Sobolev weight spaces, differential operators of elliptic type, with singular coefficients, perturbed by a potential. Conditions for compactness of embedding W s,σ r,p (Ω)↪W s,0 0,p (Ω)=L s p (Ω) for density ofD(Ω) on W s,σ r,p (Ω) and discretness conditions for the spectrum of Aσ in the Banach spaces L s p (Ω), have been established.

Entrata in Redazione il 20 dicembre 1977.

Lavoro eseguito, nell'ambito del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni del C.N.R.  相似文献   

15.
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk.  相似文献   

16.
Let m be a v-moderate function defined on R d and let gL 2(R d ). In this work, we defineΩ m p (R d ) to be the vector space of fL m 2 (R d ) such that the Gabor transform V f belongs to L p (R 2d ), where 1 ≤ p < ∞. We equip it with a norm and show that it is a Banach space with this norm. We also study some preliminary properties of Ω m p (R d ). We also discuss inclusion properties and obtain the dual space of Ω m p (R d ). At the end of this work, we study multipliers from L w 1 (R d ) into Ω w p (R d ) and from Ω w p (R d ) into L w−1 (R d ), where w is the Beurling weight function. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 139–145, January, 2006.  相似文献   

17.
We construct an unconditional basis in the Banach space L p(Ω) for p 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in ℝn. We also give an algorithm of how to construct an unconditional basis in L pp). At the end of this paper, we give the characterization of the functions in L pp) by using the wavelet coefficients.  相似文献   

18.
Lp(Rn) boundedness is considered for the multilinear singular integral operator defined by TAf(x) = ∫Rn Ω(x - y)/|x - y|n 1 (A(x) - A(y) - (△)A(y)(x - y))f(y)dy,where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈ Lipα(Sn-1) (0 <α≤ 1) and implies the Lp(Rn) (1 < p < oo) boundedness for the operator TA. Some endpoint estimates are also established.  相似文献   

19.
We derive W 2,p (Ω)-a priori estimates with arbitrary p ∈(1, ∞), for the solutions of a degenerate oblique derivative problem for linear uniformly elliptic operators with low regular coefficients. The boundary operator is given in terms of directional derivative with respect to a vector field ℓ that is tangent to ∂Ω at the points of a non-empty set ε ⊂ ∂Ω and is of emergent type on ∂Ω.   相似文献   

20.
The moments of pure imaginary and integer orders of the function L(1, χ8p), where χ8p(n) = (8p/n) and p runs over all primes p > 2, are computed. In order to derive uniform variants of the theorems on moments, the extended Riemann hypothesis for the Dirichlet L-series must be used. As corollaries, the limiting distribution of the values of log L(1, χ8p) is studied, and quantitative analogs of the Ω-results for L(1, χ8p) are obtained. Previously, Ω-results for L(1, χ8p) were proved by Bateman, Chowla, and Erdos (1949–1950) and by Barban (1966), and their methods can easily be transferred to L(1, χ8p). Bibliography: 27 titles. Dedicated to the 70th birthday of Mark Borisovich Barban __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 253–273.  相似文献   

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