Approximation by Harmonic Functions and the Dirichlet Problem

1992 ◽  
pp. 155-168 ◽  
Author(s):  
I. Netuka
Keyword(s):  
Dirichlet Problem ◽  
Harmonic Functions ◽  
Approximation By Harmonic Functions

scholarly journals Some remarks concerning harmonic functions on homogeneous graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Anders Karlsson
Keyword(s):  
Dirichlet Problem ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Cayley Graphs ◽  
Group Cohomology ◽  
Radial Variation ◽  
International Audience

International audience We obtain a new result concerning harmonic functions on infinite Cayley graphs $X$: either every nonconstant harmonic function has infinite radial variation in a certain uniform sense, or there is a nontrivial boundary with hyperbolic properties at infinity of $X$. In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. Certain relations to group cohomology are also discussed.

scholarly journals Infinite dimension of solutions of the Dirichlet problem

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Vladimir Ryazanov
Keyword(s):  
Dirichlet Problem ◽  
Unit Disk ◽  
Harmonic Functions ◽  
Infinite Dimension ◽  
Boundary Limits ◽  
Nontangential Boundary

AbstractIt is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.

scholarly journals The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities

2015 ◽  
Vol 259 (7) ◽  
pp. 3078-3114 ◽  
Author(s):  
Anders Björn ◽  
Jana Björn ◽  
Nageswari Shanmugalingam
Keyword(s):  
Dirichlet Problem ◽  
Harmonic Functions

scholarly journals Stability estimates for discrete harmonic functions on product domains

2013 ◽  
Vol 7 (1) ◽  
pp. 143-160 ◽  
Author(s):  
Maru Guadie
Keyword(s):  
Fourier Series ◽  
Dirichlet Problem ◽  
Harmonic Measure ◽  
Harmonic Functions ◽  
Discrete Analog ◽  
Stability Estimates ◽  
Product Domains ◽  
Discrete Harmonic Functions

We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragm?n-Lindel?f theorem and use Fourier series to obtain a discrete analog of the three-line theorem for the gradients of harmonic functions in a strip. Then we derive estimates for the discrete harmonic measure and use elementary spectral inequalities to obtain stability estimates for Dirichlet problem in cylinder domains.

Carleman Approximation by Harmonic Functions

1995 ◽  
Vol 117 (1) ◽  
pp. 245 ◽  
Author(s):  
Stephen J. Gardiner ◽  
Myron Goldstein
Keyword(s):  
Harmonic Functions ◽  
Carleman Approximation ◽  
Approximation By Harmonic Functions
Sign in / Sign up

Export Citation Format

Share Document