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A property of nonlinear elliptic equations when the right-hand side is a measure
Springer Science and Business Media LLC - - 1994
Central Limit Theorems for Non-Symmetric Random Walks on Nilpotent Covering Graphs: Part II
Springer Science and Business Media LLC - Tập 55 - Trang 127-166 - 2020
In the present paper, as a continuation of our preceding paper (Ishiwata et al. 2018), we study another kind of central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a view point of discrete geometric analysis developed by Kotani and Sunada. We introduce a one-parameter family of random walks which interpolates between the original non-symmetric random walk......
Branching Brownian Motions on Riemannian Manifolds: Expectation of the Number of Branches Hitting Closed Sets
Springer Science and Business Media LLC - Tập 27 - Trang 61-72 - 2007
For a branching Brownian motion on Riemannian manifold, we give an analytic criterion for the expectation of the number of branches hitting a closed set being finite.
Quantitative Heat-Kernel Estimates for Diffusions with Distributional Drift
Springer Science and Business Media LLC - Tập 59 - Trang 731-752 - 2022
We consider the stochastic differential equation on
$\mathbb {R}^{d}$
given by
$$ \begin{array}{@{}rcl@{}} \mathrm{d} X_{t} = b(t,X_{t}) \mathrm{d} t + \mathrm{d} B_{t}, \end{array} $$
where B is ......
Asymptotic Behavior of Ground States and Local Uniqueness for Fractional Schrödinger Equations with Nearly Critical Growth
Springer Science and Business Media LLC - Tập 59 - Trang 1-39 - 2021
We study quantitative aspects and concentration phenomena for ground states of the following nonlocal Schrödinger equation
$(-{\Delta })^{s} u+V(x)u= u^{2_{s}^{*}-1-\epsilon } \ \ \text {in}\ \ \mathbb {R}^{N},$
where 𝜖 > 0, s ∈ (0,1),
......
p-Energy and p-Harmonic Functions on Sierpinski Gasket Type Fractals
Springer Science and Business Media LLC - Tập 20 - Trang 125-148 - 2004
We show that it is possible to define a notion of p-energy for functions defined on a class of fractals including the Sierpinski gasket (SG) for any value of p, 1...
Finite Rank Hankel Operators over the Complex Wiener Space
Springer Science and Business Media LLC - Tập 22 - Trang 85-100 - 2005
This work studies finite rank Hankel operators Hb on a Hilbert space of holomorphic, square integrable Wiener functionals. The main tool to investigate these operators is their unitary equivalent representation on the Hilbert space of skeletons. The finite rank property is characterized in terms of a functional equation for the symbol b, which generalizes the well known equation b(z+w)=b(z)b(w). ......
Convergence of distorted Brownian motions and singular Hamiltonians
Springer Science and Business Media LLC - Tập 5 - Trang 241-271 - 1996
We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind
$$\varepsilon _\phi \left( {f,g} \right) = \tfrac{1}{2}\int_{\mathbb{R}^d } {\nabla f} \left( x \right) \cdot \nabla g\left( x \right)\phi ^2 \left( x \right)dx$$
.We obtain convergence in t......
Bismut Type Formulae for Diffusion Semigroups on Riemannian Manifolds
Springer Science and Business Media LLC - - 2006
A Montel Type Result for Super-Polyharmonic Functions on R N
Springer Science and Business Media LLC - Tập 34 - Trang 89-100 - 2010
Our aim in this paper is to discuss a Montel type result for a family
${\mathcal F}$
of super-polyharmonic functions on R
N
. We give a condition on spherical means to assure that
......
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