All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 55

Showing per page

Hardy spaces for the Laplacian with lower order perturbations

Tomasz Luks (2011)

Studia Mathematica

We consider Hardy spaces of functions harmonic on smooth domains in Euclidean spaces of dimension greater than two with respect to the Laplacian perturbed by lower order terms. We deal with the gradient and Schrödinger perturbations under appropriate Kato conditions. In this context we show the usual correspondence between the harmonic Hardy spaces and the L p spaces (or the space of finite measures if p = 1) on the boundary. To this end we prove the uniform comparability of the respective harmonic...

Harmonic measures for symmetric stable processes

Jang-Mei Wu (2002)

Studia Mathematica

Let D be an open set in ℝⁿ (n ≥ 2) and ω(·,D) be the harmonic measure on D c with respect to the symmetric α-stable process (0 < α < 2) killed upon leaving D. We study inequalities on volumes or capacities which imply that a set S on ∂D has zero harmonic measure and others which imply that S has positive harmonic measure. In general, it is the relative sizes of the sets S and D c ∖ S that determine whether ω(S,D) is zero or positive.

Harmonic measures versus quasiconformal measures for hyperbolic groups

Sébastien Blachère, Peter Haïssinsky, Pierre Mathieu (2011)

Annales scientifiques de l'École Normale Supérieure

We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.

Harnack inequality for stable processes on d-sets

Krzysztof Bogdan, Andrzej Stós, Paweł Sztonyk (2003)

Studia Mathematica

We investigate properties of functions which are harmonic with respect to α-stable processes on d-sets such as the Sierpiński gasket or carpet. We prove the Harnack inequality for such functions. For every process we estimate its transition density and harmonic measure of the ball. We prove continuity of the density of the harmonic measure. We also give some results on the decay rate of harmonic functions on regular subsets of the d-set. In the case of the Sierpiński gasket we even obtain the Boundary...

Heat diffusion on homogeneous trees (Note on a paper by G. Medolla and A. G. Setti)

Wolfgang Woess (2001)

Bollettino dell'Unione Matematica Italiana

Medolla e Setti [6] studiano l'andamento della diffusione del calore generata dal Laplaciano discreto su un albero omogeneo e dimostrano che il calore è asintoticamente concentrato in «anelli» che viaggiano verso l'infinito a velocità lineare e la cui larghezza divisa per t tende all'infinito, dove t è il tempo. Qui si spiega come un risultato più preciso si ottiene come corollario della legge dei grandi numeri e del teorema del limite centrale per la passeggiata aleatoria sull'albero. Inoltre,...

Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, Xicheng Zhang (2014)

Studia Mathematica

We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

Heat kernel estimates for the Dirichlet fractional Laplacian

Zhen-Qing Chen, Panki Kim, Renming Song (2010)

Journal of the European Mathematical Society

We consider the fractional Laplacian - ( - Δ ) α / 2 on an open subset in ℝ d with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in C 1 , 1 open sets. This heat kernel is also the transition density of a rotationally symmetric α -stable process killed upon leaving a C 1 , 1 open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.

Currently displaying 1 – 20 of 55

Page 1 Next