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1.
In Ref. 1, we considered theG-closure of some initially given arbitrary setU of the positive-definite, symmetrical plane tensorsD of the 2nd rank, connected with the differential operator ·D · in two dimensions. Here, theG-closure procedure is applied to the 4th-order operator ··D ·· in a plane, arising in the theory of plates and containing self-adjoint tensorsD of the 4th rank. The paper generalizes some results obtained earlier in Refs. 2 and 3. The complete solution of the general problem of regularization, which presupposes the arbitrary character of the initially given setU, is not yet obtained. 相似文献
2.
Peter Lindqvist 《Potential Analysis》1993,2(3):199-218
The stability with respect top of the non-linear eigenvalue problem div(|u|
p–2u)+|u|
p–2
u=0 is studied. 相似文献
3.
Tero Kilpeläinen 《Potential Analysis》1994,3(1):107-118
We consider equations like -div(|u|
p–2u)=, where is a nonnegative Radon measure and 1
u and the measure are reviewed. A link between potential estimates and the boundary regularity of the Dirichlet problem is established. 相似文献
4.
Keijo Hildén 《manuscripta mathematica》1976,18(3):215-235
A positive measurable function f on Rd can be symmetrized to a function f* depending only on the distance r, and with the same distribution function as f. If the distribution derivatives of f are Radon measures then we have the inequality f*f, where f is the total mass of the gradient. This inequality is a generalisation of the classical isoperimetric inequality for sets. Furthermore, and this is important for applications, if f belongs to the Sobolev space H1,P then f* belongs to H1,P and f*pfp. 相似文献
5.
We study the lower semicontinuous envelope in Lp(), F, of a functional F of the form F(u)=A uudx where A=A(x) is not strictly elliptic and not bounded. We prove that F; may also be written as F;(u)= Buudx with B=AP A for a matrix P which is the matrix of an orthogonal projection. In the one-dimensional case, we characterize the domain of F and we explicit the matrix P. 相似文献
6.
Bruno Chiarellotto 《Annali di Matematica Pura ed Applicata》1988,153(1):115-131
Summary We consider a 1-dimensional differential module (U, ) over an algebraic variety X. We assume the singularities of (U, ) at infinity to be separated and possibly irregular. We prove that the algebraic de Rham cohomology of X with coefficients in (U, ) can be calculated byP-adic analytic methods. 相似文献
7.
V. V. Kurta 《Ukrainian Mathematical Journal》1992,44(10):1262-1268
Analogues are formulated of the well-known, in the theory of analytic functions, Phragmen-Lindelöf theorem for the gradients of solutions of a broad class of quasilinear equations of elliptic type. Examples are given illustrating the accuracy of the results obtained for the gradients of solutions of the equations of the form div(|U|–2u)=f(x, u, u), where f(x, u, u) is a function locally bounded in 2n+1. f(x, 0, u)=0, uf(x, u, u) c¦u¦1+q(1+ ¦u|), > 1, c > 0, q > 0, is an arbitrary real number, and n >- 2. The basic role in the technique employed in the paper is played by the apparatus of capacitary characteristics.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1376–1381, October, 1992.The author sincerely appreciates E. M. Landis's permanent attention and numerous useful discussions. 相似文献
8.
We prove Lp-estimates for the Littlewood-Paley function associated with a second order divergence form operator L=–div A with bounded measurable complex coefficients in n.Mathematics Subject Classification (2000):42B20, 35J15The author is partially supported by NSF of China (Grant No. 10371134) and SRF for ROCS, SEM. 相似文献
9.
Jean -Bertrand Kammerer 《Annali di Matematica Pura ed Applicata》1985,142(1):215-261
Summary
The purpose of this paper is to study, in intrinsic way, the Moyal's product, defined in the flat space
R
2n. This product is defined here with the twisted convolution and the Fourier transform. The S(R
2n) and L2(R
2n) spaces are*5-algebras. Because of this definition, the*V-product of some tempered distributions is defined. Let O
M
v
be the set of multiplication operators in S(R
2n). By transposition, the S(R
2n) space is a right-module on O
M
v
. The support of f*v g is different from the support of f·g; under large enough hypotheses, there is a Taylor's formula for the star-product function of the v variable. The v space of the multiplication operators in L2(R
2n) is defined here as the space of tempered distributions, the image of which is the set of bounded operators in L2(R
2n) by the Weyl map. After the study of v space, it is possible to show the spectral resolution of the real elements of v or of O
M
v
, which satisfies a, probably superfluous, hypothesis. 相似文献
10.
Summary This paper considers the finite element approximation of the semi-definite Neumann problem: –·(u)=f in a curved domain
n
(n=2 or 3),
on and
, a given constant, for dataf andg satisfying the compatibility condition
. Due to perturbation of domain errors (
h
) the standard Galerkin approximation to the above problem may not have a solution. A remedy is to perturb the right hand side so that a discrete form of the compatibility condition holds. Using this approach we show that for a finite element space defined overD
h
, a union of elements, with approximation powerh
k
in theL
2 norm and with dist (,
h
)Ch
k
, one obtains optimal rates of convergence in theH
1 andL
2 norms whether
h
is fitted (
h
D
h
) or unfitted (
h
D
h
) provided the numerical integration scheme has sufficient accuracy.Partially supported by the National Science Foundation, Grant #DMS-8501397, the Air Force Office of Scientific Research and the Office of Naval Research 相似文献
11.
We consider the vector Riesz transform t-(t+s)/2 divs of even order s + t in the weighted space L
2(n;|x|a). We establish that for t s, n >3 its norm is equal to one on some interval of values of a, while inside the interval a stronger estimate for a subordinate norm is valid. 相似文献
12.
The decycling number, (G), of a graph G is the least number of vertices of G whose deletion results in an induced subgraph without any cycles. Improved bounds are obtained for the decycling number (Q
n
) of the hypercube Q
n
. Further, it is shown that (Q
n
)=2
n
–1–A(n,4) if and only if Q
n
has a minimum decycling set that consists of pairwise non-adjacent vertices, where A(n,4) denotes the size of a maximum binary code of length n and minimum Hamming distance 4.
Research supported by NSERC 相似文献
13.
A. Moór 《Periodica Mathematica Hungarica》1982,13(2):129-135
In this note necessary and sufficient conditions are determined for Weyl—tsukispaces to have a birecurrent metric, i.e.,
m
k
g
ij
=
km
g
ij
. It is proved that in this space the metric tensor is an eigen-tensor. The special caseP
j
i
= (x)
j
i
is examined and we prove that in this case the recurrent metric tensor is likewise birecurrent. 相似文献
14.
Soit X une diffusion uniformément elliptique sur R
d
,F une fonction dans H
loc
1(R
d
) et la loi initiale de la diffusion. On montre que si l'intégrale |F|2(x)U(x)dx est finie, oùU désigne le potentiel de la mesure , alors F(X) est un processus de Dirichlet. Si de plus, F appartient àH
2
loc(R
d
) et si les intégrales |F|2(x)U(x)dx et |f
k
|2(x)U(x)dx sont finies, pour les dérivées faibles f
k
de F, alors on peut écrire une formule d'Itô. En particulier, on définit l'intégrale progressive F(X)dX et on prouve l'existence des covariations quadratiques [f
k
(X),X
k
]. 相似文献
15.
Two main properties of the subgradient mapping of convex functions are transposed for quasiconvex ones. The continuity of the functionxf(x)–1f(x) on the domain where it is defined is deduced from some continuity properties of the normal coneN to the level sets of the quasiconvex functionf. We also prove that, under a pseudoconvexity-type condition, the normal coneN(x) to the set {x:f(x)f(x)} can be expressed as the convex hull of the limits of type {N(x
n)}, where {x
n} is a sequence converging tox and contained in a dense subsetD. In particular, whenf is pseudoconvex,D can be taken equal to the set of points wheref is differentiable.This research was completed while the second author was on a sabbatical leave at the University of Montreal and was supported by a NSERC grant. It has its origin in the doctoral thesis of the first author (Ref. 1), prepared under the direction of the second author.The authors are grateful to an anonymous referee and C. Zalinescu for their helpful remarks on a previous version of this paper. 相似文献
16.
This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. 相似文献
17.
Wolfgang Krieger 《Probability Theory and Related Fields》1969,11(2):83-97
We consider a Lebesgue measure space (M, , m). By an automorphism of (M, , m) we mean a bi-measurable transformation of (M, , m) that together with its inverse is non-singular with respeot to m. We study an equivalence relation between these automorphisms that we call the weak equivalence. Two automorphisms S and T are weakly equivalent if there is an automorphism U such that for almost all x M U maps the S-orbit of x onto the T-orbit of U x. Ergodicity, the existence of a finite invariant measure, the existenoe of a -finite infinite invariant measure, and the non-existence of such measures are invariants of weak equivalenoe. In this paper and in its sequel we solve the problem of weak equivalenoe for a class of automorphisms that comprises all ergodic automorphisms that admit a -finite invariant measure, and also certain ergodic automorphisms that do not admit such a measure. 相似文献
18.
Alan D. Sokal 《Probability Theory and Related Fields》1981,56(4):537-548
Summary Let (, , ) be a perfect probability space with countably generated, and let IB be a family of sub--fields of . Under a countability condition on the family IB, I show that there exists a family {}IB of regular conditional probabilities which are everywhere compatible. Under a more stringent condition on IB, I show that the
can furthermore be chosen to be everywhere proper. It follows that in the Dobrushin-Lanford-Ruelle formulation of the statistical mechanics of classical lattice systems, every (perfect) probability measure is a Gibbs measure for some specification.Research supported in part by NSF PHY-78-23952NSF Predoctoral Fellow (1976–79) and Danforth Fellow (1979–81). 相似文献
19.
N. Filonov 《Journal of Mathematical Sciences》2001,106(3):3078-3086
An equation of the form -div (gu) = u has a solution u of class C
0
, where g is a real positive definite matrix-valued function belonging to the Holder classes with exponent less than 1. From the spectral point of view, this means that there exists a Schrodinger operator with periodic metric and the spectrum of this operator contains an eigenvalue of infinite multiplicity. Bibliography: 9 titles. 相似文献
20.
In this paper we study the question of uniqueness for an inverse problem, arising in the (thermal) linear and/or non-linear potential theory. The overdetermined problem we shall study is represented by(div(|u|
p–2u)–D
t
u–+)u=0where supp()R
n
×(0,), 1<p<, L
and {t=} is bounded for >0.The problem has applications in shape-recognition in underground water/oil recovery, subject to shape-change during time intervals. The particular case u0, D
t
u0, and p=2, is an example of the well-known Stefan. 相似文献