共查询到20条相似文献,搜索用时 15 毫秒
1.
A gradient-entropy inequality is established for elliptic diffusion semigroups on arbitrary complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived. 相似文献
2.
Enrico Priola 《Journal of Evolution Equations》2006,6(4):577-600
We consider the diffusion semigroup Pt associated to a class of degenerate elliptic operators
. This class includes the hypoelliptic Ornstein-Uhlenbeck operator but does not satisfy in general the well-known H?rmander
condition on commutators for sums of squares of vector fields. We establish probabilistic formulae for the spatial derivatives
of Pt f up to the third order. We obtain L∞-estimates for the derivatives of Pt f and show the existence of a classical bounded solution for the parabolic Cauchy problem involving
and having
as initial datum.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
3.
Liang Zhao 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):433-443
4.
Proximal Calculus on Riemannian Manifolds 总被引:2,自引:0,他引:2
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold
M. We give some applications of this theory, concerning, for instance, a Borwein-Preiss type variational principle on a Riemannian
manifold M, as well as differentiability and geometrical properties of the distance function to a closed subset C of M.
The first-named author was supported by a Marie Curie Intra-European Fellowship of the European Community, Human Resources
and Mobility Programme under contract number MEIF CT2003-500927. The second-named author was supported by BFM2003-06420. 相似文献
5.
In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the -condition, where and are two constants. Moreover, we introduce the W-entropy and prove the W-entropy formula for the fundamental solution of the Witten Laplacian on complete Riemannian manifolds with the -condition and on compact manifolds equipped with -super Ricci flows. 相似文献
6.
We prove short time estimates for the heat kernel of Schr?dinger operators with unbounded potential in RN. 相似文献
7.
Marc Arnaudon 《Bulletin des Sciences Mathématiques》2006,130(3):223
Using the coupling by parallel translation, along with Girsanov's theorem, a new version of a dimension-free Harnack inequality is established for diffusion semigroups on Riemannian manifolds with Ricci curvature bounded below by , where c>0 is a constant and ρo is the Riemannian distance function to a fixed point o on the manifold. As an application, in the symmetric case, a Li-Yau type heat kernel bound is presented for such semigroups. 相似文献
8.
We discuss in polar coordinates the relation between unitarizing measures and invariant measures for the Ornstein-Uhlenbeck operator in the Poincaré disk. Then we study the Ornstein-Uhlenbeck operator in terms of the vector fields of the modular representation. 相似文献
9.
Conformal deformations on a noncompact Riemannian manifold 总被引:3,自引:0,他引:3
Ma Li 《Mathematische Annalen》1993,295(1):75-80
10.
Luís Almeida 《Calculus of Variations and Partial Differential Equations》1995,3(2):193-242
Let be a Riemannian surface and
be a standard sphere, or more generally a Riemannian manifold on which a Lie group,, acts transitively by isometries. We define generalized harmonic maps by extending the notion of weakly harmonic maps in a natural way (motivated by Noether's Theorem), to mapsu W
loc
1,1
(,
). We prove that, under some slight technical restrictions, for 1 <-p < 2, there are generalized harmonic mapsu W
1,p(,
) that are everywhere discontinuous (in particular, this solves an open problem proposed by F. Bethuel, H. Brezis and F. Hélein, in [BBH]). We also show that the natural -regularity condition for such maps is to require <u to belong to the Lorentz space L(2, ). To prove this -regularity result we extend a compensated compactness result of R. Coifman, P.-L. Lions, Y. Meyer and S. Semmes, proved in [CLMS], to the case of Lorentz spaces in duality. 相似文献
11.
Lorenzo Zambotti 《Journal of Functional Analysis》2005,223(1):147-178
We prove an integration by parts formula on the law of the reflecting Brownian motion in the positive half line, where B is a standard Brownian motion. In other terms, we consider a perturbation of X of the form Xε=X+εh with h smooth deterministic function and ε>0 and we differentiate the law of Xε at ε=0. This infinitesimal perturbation changes drastically the set of zeros of X for any ε>0. As a consequence, the formula we obtain contains an infinite-dimensional generalized functional in the sense of Schwartz, defined in terms of Hida's renormalization of the squared derivative of B and in terms of the local time of X at 0. We also compute the divergence on the Wiener space of a class of vector fields not taking values in the Cameron-Martin space. 相似文献
12.
In this paper, we successfully generalize the eigenvalue comparison theorem for the Dirichlet p -Laplacian (1<p<∞) obtained by Matei (2000) [19] and Takeuchi (1998) [22], respectively. Moreover, we use this generalized eigenvalue comparison theorem to get estimates for the first eigenvalue of the Dirichlet p-Laplacian of geodesic balls on complete Riemannian manifolds with radial Ricci curvature bounded from below w.r.t. some point. In the rest of this paper, we derive an upper and lower bound for the heat kernel of geodesic balls of complete manifolds with specified curvature constraints, which can supply new ways to prove the most part of two generalized eigenvalue comparison results given by Freitas, Mao and Salavessa (2013) [9]. 相似文献
13.
In this paper, we consider the problem (Pε) : Δ2u=un+4/n-4+εu,u>0 in Ω,u=Δu=0 on ∂Ω, where Ω is a bounded and smooth domain in Rn,n>8 and ε>0. We analyze the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev inequality as ε→0 and we prove existence of solutions to (Pε) which blow up and concentrate around a critical point of the Robin's function. Finally, we show that for ε small, (Pε) has at least as many solutions as the Ljusternik–Schnirelman category of Ω. 相似文献
14.
In this paper we consider radially symmetric solutions of the nonlinear Dirichlet problem Δu+f(|x|,u)=0 in Ω, where Ω is a ball in RN, N?3 and f satisfies some appropriate assumptions. We prove existence of radially symmetric solutions with k prescribed number of zeros. Moreover, when f(|x|,u)=K(|x|)|u|p−1u, using the uniqueness result due to Tanaka (2008) [21], we verify that these solutions are non-degenerate and we prove that their radial Morse index is exactly k. 相似文献
15.
Xiang-Dong Li 《Probability Theory and Related Fields》2008,141(1-2):247-281
Under the condition that the Bakry–Emery Ricci curvature is bounded from below, we prove a probabilistic representation formula
of the Riesz transforms associated with a symmetric diffusion operator on a complete Riemannian manifold. Using the Burkholder
sharp L
p
-inequality for martingale transforms, we obtain an explicit and dimension-free upper bound of the L
p
-norm of the Riesz transforms on such complete Riemannian manifolds for all 1 < p < ∞. In the Euclidean and the Gaussian cases, our upper bound is asymptotically sharp when p→ 1 and when p→ ∞.
Research partially supported by a Delegation in CNRS at the University of Paris-Sud during the 2005–2006 academic year. 相似文献
16.
Jun Kigami 《Mathematische Annalen》2008,340(4):781-804
We study the standard Dirichlet form and its energy measure,called the Kusuoka measure, on the Sierpinski gasket as aprototype
of “measurable Riemannian geometry”. The shortest pathmetric on the harmonic Sierpinski gasket is shown to be thegeodesic
distance associated with the “measurable Riemannianstructure”. The Kusuoka measure is shown to have the volumedoubling property
with respect to the Euclidean distance and alsoto the geodesic distance. Li–Yau type Gaussian off-diagonal heatkernel estimate
is established for the heat kernel associated withthe Kusuoka measure. 相似文献
17.
For free boundary problems on Euclidean spaces, the monotonicity formulas of Alt–Caffarelli–Friedman and Caffarelli–Jerison–Kenig are cornerstones for the regularity theory as well as the existence theory. In this article we establish the analogs of these results for the Laplace–Beltrami operator on Riemannian manifolds. As an application we show that our monotonicity theorems can be employed to prove the Lipschitz continuity for the solutions of a general class of two-phase free boundary problems on Riemannian manifolds. 相似文献
18.
19.
We prove Cheng–Yau type inequalities for positive harmonic functions on Riemannian manifolds by using methods of Stochastic Analysis. Rather than evaluating an exact Bismut formula for the differential of a harmonic function, our method relies on a Bismut type inequality which is derived by an elementary integration by parts argument from an underlying submartingale. It is the monotonicity inherited in this submartingale which allows us to establish the pointwise estimates. 相似文献
20.
We reexamine bifurcation questions for potential operators. Based on the Conley index theory we present a unified approach
to bifurcations both at the origin and at infinity. Our results provide improvements of the existing theory. 相似文献