Dirichlet Problem for Functions that are Harmonic on a Two-Dimensional Net
نویسندگان
چکیده
In this paper, we consider the Dirichlet problem for harmonic functions on a two-dimensional complex of special type. We prove that is Fredholm in Hölder class and its index zero.
منابع مشابه
Two-dimensional multiple-valued Dirichlet minimizing functions
We give some remarks on two-dimensional multiple-valued Dirichlet minimizing functions, including frequency, classification of branch points and their connections. As an application, we prove that blowing-up functions of a two-dimensional multiple-valued Dirichlet minimizing function are unique. This paper is concluded with a boundary regularity theorem for two-dimensional multiple-valued Diric...
متن کاملOn the Dirichlet Problem for Harmonic Maps with Prescribed Singularities
Let (M, g) be a classical Riemannian globally symmetric space of rank one and non-compact type. We prove the existence and uniqueness of solutions to the Dirichlet problem for harmonic maps into (M, g) with prescribed singularities along a closed submanifold of the domain. This generalizes our previous work where such maps into the hyperbolic plane were constructed. This problem, in the case wh...
متن کاملExistence Results for a Dirichlet Quasilinear Elliptic Problem
In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.
متن کاملInvariant 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 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 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: Journal of Mathematical Sciences
سال: 2021
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-021-05468-2