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简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合,以简单的随机微分方程为例,将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
Let M be a complete non-compact Riemannian manifold. For p ∈ (1,+∞), let Δp be the p-Laplace operator on M. One says that M is p-hyperbolic if there exists a Green function for Δp (see [Ho1,2]); oth...
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity.While our previous work [IKR] considered the elliptic case, here we treat the more ch...
In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a techn...
By constructing a coupling in two steps and using the Girsanov theorem under a regular conditional probability, the log-Harnack inequality is established for a large class of Gruschin type semigroups ...
We discuss the problem how "bad" may be lower-order coefficients in elliptic and parabolic second order equations to ensure some qualitative properties of solution such as strong maximum principle, H...
By proving an L2-gradient estimate for the corresponding Galerkin approximations,the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As a...
We study linear time fractional diffusion equations in divergence form of time order less than one. It is merely assumed that the coefficients are measurable and bounded, and that they satisfy a unifo...

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