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991.
Gioconda?MoscarielloEmail author 《NoDEA : Nonlinear Differential Equations and Applications》2004,11(3):393-406
We prove a higher integrability result for the gradient of solutions to some degenerate elliptic PDEs, whose model arises in the study of mappings with finite distortion.The nonnegative function
which measures the degree of degeneracy of ellipticity bounds lies in the exponential class, i.e.
is integrable for some > 0.Our result states that if is sufficiently large, then the gradient of a finite energy solution actually belongs to the Zygmund space LplogL, 1. 相似文献
992.
Here we study a nonlinear hyperbolic integrodifferential system which was proposed by H.G. Rotstein et al. to
describe certain peculiar phase
transition phenomena. This system governs the evolution of the (relative) temperature and the order parameter (or phase-field)
. We first consider an initial and boundary value problem associated with the system and we frame it in a history space setting.
This is done by introducing two additional variables accounting for the histories of and . Then we show that the reformulated problem
generates a dissipative dynamical system in a suitable infinite-dimensional phase space. Finally, we prove the existence of a universal attractor. 相似文献
993.
This note is concerned with the initial value problem for the abstract
nonlocal equation
where A is a
maximal monotone operator from a reflexive Banach space E to its
dual E*, while B is a
nonlocal maximal monotone operator from
.
Under proper boundedness and coercivity assumptions on the operators, a solution is achieved by means of a discretization
argument. Uniqueness and continuous dependence are also discussed and we prove some estimates for the discretization
error. Finally, we deal with the approximation of linear Volterra integrodifferential operators. 相似文献
994.
Piermarco?CannarsaEmail author Daniela?SforzaEmail author 《Mediterranean Journal of Mathematics》2004,1(2):151-174
The main object of this work is the existence of global solutions to semilinear integrodifferential equations in Hilbert spaces for absolutely continuous convolution kernels, where the nonlinear term is the gradient of a functional having superlinear growth at infinity. An application to the theory of viscoelasticity concludes the paper providing motivations for the abstract theory. 相似文献
995.
Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》2001,50(3):393-404
LetG be a group and α an automorphism ofG; α is calledn-splitting if
for allg∈G. In this note we study the structure of finite groups admitting an-splitting automorphism of order 2.
相似文献
996.
Kim Plofker 《Historia Mathematica》2001,28(4):283
It has been repeatedly noted, but not discussed in detail, that certain so-called “third-order Taylor series approximations” found in the school of the medieval Keralese mathematician M
dhava are inaccurate. That is, these formulas, unlike the other series expansions brilliantly developed by M
dhava and his followers, do not correspond exactly to the terms of the power series subsequently discovered in Europe, by whose name they are generally known. We discuss a Sanskrit commentary on these rules that suggests a possible derivation explaining this discrepancy, and in the process re-emphasize that the Keralese work on such series was rooted in geometric approximation rather than in analysis per se. © 2001 Elsevier Science (USA).Es ist mehrfach festgestellt bisher aber nicht ausführlich diskutiert worden, daß einige sogenannte Taylor-reihennäherungswerte dritter Ordnung, die in der mittelalterlichen Schule keralesischen M
dhava gefunden werden, ungenau sind. Das heißt, diesc Formeln sind den Termen der Potenzreihe, die später in Europa entwickelt wurde und unter dem Namen Taylorreihe bekannt ist, nicht äquivalent, im Gegensatz zu den anderen Entwicklungen von Reihen, die glänzend von M
dhava und seinen Nachfolgern entwickelt werden. Wir behandeln einen Sanskritkommentar zu den Regeln, der eine mögliche Herleitung suggeriert, die diese Diskrepanz erklärt. Dabei betonen wir nochmals, daß die keralesische Arbeit über solche Reihen eher in geometrischen Näherungen als in der Analysis an sich ihre Wurzeln hat. © 2001 Elsevier Science (USA).MSC subject classification: 01A32. 相似文献
997.
Henry C. Wente 《Journal of Mathematical Fluid Mechanics》2008,10(4):583-587
In capillary theory there are two kinds of surface tension. There is the surface tension at the interface between two immiscible
fluids. Thomas Young [9] also allowed for there to be a surface tension associated with a liquid-solid interface. He proceeded
to use a balance of forces argument to derive the well-known contact angle condition along a liquid-liquid-solid intersection.
The validity of this argument has recently been called into question by R. Finn [6]. A floating ball experiment discussed
in that paper leads to an apparent paradox. We address this issue.
相似文献
998.
Stochastic Linear Quadratic Optimal Control Problems 总被引:2,自引:0,他引:2
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the
coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control
variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward—backward
stochastic differential equations are established. Some results involving Riccati equation are discussed as well.
Accepted 15 May 2000. Online publication 1 December 2000 相似文献
999.
Ravi Vakil 《Mathematische Annalen》2001,320(1):33-54
The following divisors in the space of twelve points on are actually the same: the possible locus of the twelve nodal fibers in a rational elliptic fibration (i.e. a pencil of plane cubic curves); degree 12 binary forms that can be expressed as a cube plus a square; the locus of the twelve tangents to a smooth plane quartic from a general point of the plane; the branch locus of a degree 4 map from a hyperelliptic genus 3 curve to ; the branch locus of a degree 3 map from a genus 4 curve to induced by a theta-characteristic; and several more. The corresponding moduli spaces are smooth, but they are not all isomorphic;
some are finite étale covers of others. We describe the web of interconnections among these spaces, and give monodromy, rationality,
and Prym-related consequences. Enumerative consequences include: (i) the degree of this locus is 3762 (e.g. there are 3762
rational elliptic fibrations with nodes above 11 given general points of the base); (ii) if is a cover as in , then there are 135 different such covers branched at the same points; (iii) the general set of 12 tangent lines that arise
in turn up in 120 essentially different ways. Some parts of this story are well known, and some other parts were known classically
(to Zeuthen, Zariski, Coble, Mumford, and others). The unified picture is surprisingly intricate and connects many beautiful
constructions, including Recillas' trigonal construction and Shioda's -Mordell-Weil lattice.
Received November 3, 1999 / Published online February 5, 2001 相似文献
1000.
Siniša Slijepčevič 《Mathematische Zeitschrift》2001,237(3):469-504
If F is an exact symplectic map on the{\it d}-dimensional cylinder , with a generating function h having superlinear growth and uniform bounds on the second derivative, we construct a strictly gradient semiflow on the space of shift-invariant probability measures on the space of configurations . Stationary points of are invariant measures of F, and the rotation vector and all spectral invariants are invariants of . Using and the minimisation technique, we construct minimising measures with an arbitrary rotation vector , and with an additional assumption that F is strongly monotone, we show that the support of every minimising measure is a graph of a Lipschitz function. Using and the relaxation technique, assuming a weak condition on (satisfied e.g. in Hedlund's counter-example, and in the anti-integrable limit) we show existence of double-recurrent orbits
of F (and F-ergodic measures) with an arbitrary rotation vector , and action arbitrarily close to the minimal action .
Received November 4, 1999; in final form July 29, 2000 / Published online April 12, 2001 相似文献