Dirichlet problems of harmonic functions
نویسندگان
چکیده
منابع مشابه
Invariant Percolation and Harmonic Dirichlet Functions
The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of BenjaminiLyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those on the infinite clusters in the uniqueness phase of Bernoulli percolation. We extend the result to more general invariant percolations, including the Random-Cluster model. We prove the existence of the nonuniqueness phase f...
متن کاملHarmonic Polynomials and Dirichlet-Type Problems
We take a new approach to harmonic polynomials via differentiation. Surprisingly powerful results about harmonic functions can be obtained simply by differentiating the function |x|2−n and observing the patterns that emerge. This is one of our main themes and is the route we take to Theorem 1.7, which leads to a new proof of a harmonic decomposition theorem for homogeneous polynomials (Corollar...
متن کاملRough Isometries and Dirichlet Finite Harmonic Functions on Graphs
Suppose that G\ and G% are roughly isometric connected graphs of bounded degree. If G\ has no nonconstant Dirichlet finite harmonic functions, then neither has Gi.
متن کاملOn Roughly Transitive Amenable Graphs and Harmonic Dirichlet Functions
We introduce the notion of rough transitivity and prove that there exist no non-constant harmonic Dirichlet functions on amenable roughly transitive graphs.
متن کاملSolution of Harmonic Problems with Weak Singularities Using Equilibrated Basis Functions in Finite Element Method
In this paper, Equilibrated Singular Basis Functions (EqSBFs) are implemented in the framework of the Finite Element Method (FEM), which can approximately satisfy the harmonic PDE in homogeneous and heterogeneous media. EqSBFs are able to automatically reproduce the terms consistent with the singularity order in the vicinity of the singular point. The newly made bases are used as the compliment...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2013
ISSN: 1687-2770
DOI: 10.1186/1687-2770-2013-262