Harnack's inequality and Green functions on locally finite graphs

نویسنده

  • Li Ma
چکیده

In this paper we study the gradient estimate for positive solutions of Schrodinger equations on locally finite graph. Then we derive Harnack’s inequality for positive solutions of the Schrodinger equations. We also set up some results about Green functions of the Laplacian equation on locally finite graph. Interesting properties of Schrodinger equation are derived. Mathematics Subject Classification 2000: 31C20, 31C05

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Alexandroff topology on graphs

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

متن کامل

On the Graphs Related to Green Relations of Finite Semigroups

In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first atte...

متن کامل

A notion of continuity in discrete spaces and applications

We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs. We use this notion of continuity to derive an analogue in Z of the Jordan curve theorem and to extend to a quite large class of locally finite metric spaces (containing all finite metric spaces) an inequality for the l-distortio...

متن کامل

Brownian Motion and a Consequence of Harnack's Inequality: Nodes of Quantum Wave Functions'

Using Brownian motion ideas, we give two proofs that for a large class of V's, (-A + V)u = Eu and u(x,,) = 0 implies that u changes sign near xo.

متن کامل

REMO GARATTINI Harnack’s Inequality on Homogeneous Spaces

We consider a homogeneous space X = (X, d, m) of dimension ν ≥ 1 and a local regular Dirichlet form in L 2 (X, m). We prove that if a Poincaré inequality holds on every pseudo-ball B (x, R) of X, then an Harnack's inequality can be proved on the same ball with local characteristic constant c 0 and c 1

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/1310.8390  شماره 

صفحات  -

تاریخ انتشار 2013