共查询到20条相似文献,搜索用时 15 毫秒
1.
Giuseppe Da Prato Arnaud Debussche Beniamin Goldys 《Probability Theory and Related Fields》2002,123(3):355-380
We consider transition semigroups generated by stochastic partial differential equations with dissipative nonlinear terms.
We prove an integration by part formula and a Logarithmic Sobolev inequality for the invariant measure. No symmetry or reversibility
assumptions are made. Furthemore we prove some compactness results on the transition semigroup and on the embedding of the
Sobolev spaces based on the invariant measure. We use these results to derive asymptotic properties for a stochastic reaction–diffusion
equation.
Received: 29 September 2000 / Revised version: 30 May 2001 / Published online: 14 June 2002 相似文献
2.
We study the Palais-Smale sequence relative to the two-dimensional Trudinger-Moser inequality. First, we show that such a
sequence concentrates to finite points if it is not compact in H1. Then, under an additional condition, the singular limit is specified in use of the Green's function.
Received: 8 April 2001 / Accepted: 8 May 2002 / Published online: 5 September 2002 相似文献
3.
Georgios K. Alexopoulos 《Probability Theory and Related Fields》2002,124(1):112-150
We study the asymptotic behavior of the convolution powers of a centered density on a connected Lie group G of polynomial volume growth. The main tool is a Harnack inequality which is proved by using ideas from Homogenization theory
and by adapting the method of Krylov and Safonov. Applying this inequality we prove that the positive -harmonic functions are constant. We also characterise the -harmonic functions which grow polynomially. We give Gaussian estimates for , as well as for the differences and . We give estimates, similar to the ones given by the classical Berry-Esseen theorem, for and . We use these estimates to study the associated Riesz transforms.
Received: 5 July 1999 / Revised version: 8 April 2002 / Published online: 22 August 2002 相似文献
4.
We show that the -parabolic Harnack inequality for random walks on graphs is equivalent, on one hand, to the sub-Gaussian estimate for the
transition probability and, on the other hand, to the conjunction of the elliptic Harnack inequality, the doubling volume
property, and the fact that the mean exit time in any ball of radius R is of the order . The latter condition can be replaced by a certain estimate of the resistance of annuli.
Received: 15 November 2001 / Revised version: 21 February 2002 / Published online: 6 August 2002 相似文献
5.
Thorsten Thies 《manuscripta mathematica》2003,111(1):97-104
We prove an isoperimetric inequality for compact, regular domains in rank one symmetric spaces, which is sharp for geodesic
balls. Besides volume and area of a given domain, some weak information about the second fundamental form of its boundary
is involved.
Received: 2 September 2002 / Revised version: 10 December 2002
Published online: 20 March 2003
Mathematics Subject Classification (2000): 53C35, 52A40, 51M25 相似文献
6.
Henri Anciaux 《Mathematische Zeitschrift》2002,241(3):639-664
We compute loops integrals on Hamiltonian stationary Lagrangian tori in which are symplectic invariants, then we show an isoperimetric inequality involving these invariants and the area. Finally,
we show that the flat torus has least area among Hamiltonian stationary Lagrangian tori of its isotopy class.
Received: 4 December 2000; in final form: 18 January 2002 / Published online: 5 September 2002 相似文献
7.
Tadahisa Funaki 《Probability Theory and Related Fields》2003,126(2):155-183
We consider random evolution of an interface on a hard wall under periodic boundary conditions. The dynamics are governed
by a system of stochastic differential equations of Skorohod type, which is Langevin equation associated with massless Hamiltonian
added a strong repelling force for the interface to stay over the wall. We study its macroscopic behavior under a suitable
large scale space-time limit and derive a nonlinear partial differential equation, which describes the mean curvature motion
except for some anisotropy effects, with reflection at the wall. Such equation is characterized by an evolutionary variational
inequality.
Received: 10 January 2002 / Revised version: 18 August 2002 /
Published online: 15 April 2003
Mathematics Subject Classification (2000): 60K35, 82C24, 35K55, 35K85
Key words or phrases: Hydrodynamic limit – Effective interfaces – Hard wall – Skorohod's stochastic differential equation – Evolutionary variational
inequality 相似文献
8.
S.M. Natanzon 《Mathematische Zeitschrift》2003,243(2):391-407
Let Y be a complex algebraic curve and let be the set of all real algebraic curves with complexification , such that the real points divide . We find all such families [Y]. According to Harnak theorem a number of connected components of satisfies by the inequality , where g is the genus of Y. We prove that and these estimates are exact.
Received: 15 November 2001; in final form: 28 April 2002/Published online: 2 December 2002 相似文献
9.
We describe a procedure for constructing ”polar coordinates” in a certain class of Carnot groups. We show that our construction
can be carried out in groups of Heisenberg type and we give explicit formulas for the polar coordinate decomposition in that
setting. The construction makes use of nonlinear potential theory, specifically, fundamental solutions for the p-sub-Laplace operators. As applications of this result we obtain exact capacity estimates, representation formulas and an
explicit sharp constant for the Moser-Trudinger inequality. We also obtain topological and measure-theoretic consequences
for quasiregular mappings.
Received: 26 June 2001; in final form: 14 January 2002/Published online: 5 September 2002 相似文献
10.
Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for
the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration
phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper
bounds on spectral gaps.
Received: 10 June 1996 / In revised form: 9 August 1996 相似文献
11.
Abstract We study Harnack type properties of quasiminimizers of the
-Dirichlet integral on metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality. We show
that an increasing sequence of quasiminimizers converges locally uniformly to a quasiminimizer, provided the limit function
is finite at some point, even if the quasiminimizing constant and the boundary values are allowed to vary in a bounded way.
If the quasiminimizing constants converge to one, then the limit function is the unique minimizer of the
-Dirichlet integral. In the Euclidean case with the Lebesgue measure we obtain convergence also in the Sobolev norm.
Keywords: Metric space, doubling measure, Poincaré inequality, Newtonian space, Harnack inequality, Harnack convergence theorem
Mathematics Subject Classification (2000): 49J52, 35J60, 49J27 相似文献
12.
J. Chabrowski M. Willem 《Calculus of Variations and Partial Differential Equations》2002,15(4):421-431
We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least
energy solutions. As a by-product we establish a Sobolev inequality with interior norm.
Received: 26 April 2000 / Accepted: 25 February 2001 / Published online: 5 September 2002 相似文献
13.
14.
We give an “elementary” proof of an inequality due to Maz’ya. As a prerequisite we prove an approximation property for the Hausdorff measure. We also comment on the relations between Maz’ya’s inequality, the isoperimetric inequality, and the Sobolev inequality. 相似文献
15.
Botjan Brear Wilfried Imrich Sandi Klavar Henry Martyn Mulder Riste krekovski 《Journal of Graph Theory》2002,40(2):91-103
In the quest to better understand the connection between median graphs, triangle‐free graphs and partial cubes, a hierarchy of subclasses of partial cubes has been introduced. In this article, we study the role of tiled partial cubes in this scheme. For instance, we prove that almost‐median graphs are tiled and that tiled partial cubes are semi‐median. We also describe median graphs as tiled partial cubes without convex Q and extend an inequality for median graphs to a larger subclass of partial cubes. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 91–103, 2002 相似文献
16.
Machiel van Frankenhuijsen 《Journal of Number Theory》2007,127(2):292-300
The truncated or radicalized counting function of a meromorphic function counts the number of times that f takes a value a, but without multiplicity. By analogy, one also defines this function for numbers. In this sequel to [M. van Frankenhuijsen, The ABC conjecture implies Vojta's height inequality for curves, J. Number Theory 95 (2002) 289-302], we prove the radicalized version of Vojta's height inequality, using the ABC conjecture. We explain the connection with a conjecture of Serge Lang about the different error terms associated with Vojta's height inequality and with the radicalized Vojta height inequality. 相似文献
17.
S. Artstein-Avidan B. Klartag C. Schütt E. Werner 《Journal of Functional Analysis》2012,262(9):4181-4204
We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincaré inequality for the Gaussian measure. 相似文献
18.
Estibalitz Durand-Cartagena Nageswari Shanmugalingam Alex Williams 《Mathematische Zeitschrift》2012,271(1-2):447-467
We point out some of the differences between the consequences of p-Poincaré inequality and that of ∞-Poincaré inequality in the setting of doubling metric measure spaces. Based on the geometric characterization of ∞-Poincaré inequality given in Durand-Cartagena et al. (Mich Math J 60, 2011), we obtain a geometric property implied by the support of a p-Poincaré inequality, and demonstrate by examples that an analogous geometric characterization for finite p is not possible. The examples we give are metric measure spaces which are doubling and support an ∞-Poincaré inequality, but support no finite p-Poincaré inequality. In particular, these examples show that one cannot expect a self-improving property for ∞-Poincaré inequality in the spirit of Keith–Zhong (Ann Math 167(2):575–599, 2008). We also show that the persistence of Poincaré inequality under measured Gromov–Hausdorff limits fails for ∞-Poincaré inequality. 相似文献
19.
Ferenc Mó ricz Ká roly Tandori 《Proceedings of the American Mathematical Society》1996,124(3):877-885
We study the a.e. convergence of orthogonal series defined over a general measure space. We give sufficient conditions which contain the Menshov-Rademacher theorem as an endpoint case. These conditions turn out to be necessary in the particular case where the measure space is the unit interval and the moduli of the coefficients form a nonincreasing sequence. We also prove a new version of the Menshov-Rademacher inequality.
20.
This work concerns constructive aspects of measure theory. By considering metric completions of Boolean algebras – an approach
first suggested by Kolmogorov – one can give a very simple construction of e.g. the Lebesgue measure on the unit interval.
The integration spaces of Bishop and Cheng turn out to give examples of such Boolean algebras. We analyse next the notion
of Borel subsets. We show that the algebra of such subsets can be characterised in a pointfree and constructive way by an
initiality condition. We then use our work to define in a purely inductive way the measure of Borel subsets.
Received: 9 November 2000 / Revised version: 23 March 2001 / Published online: 12 July 2002 相似文献