Boundary value problems on planar graphs and flat surfaces with integer cone singularities, II: The mixed Dirichlet-Neumann problem

Sa'ar Hersonsky

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this paper we continue the study started in Hersonsky (in press) [16]. We consider a planar, bounded, m-connected region Ω, and let ∂ Ω be its boundary. Let T be a cellular decomposition of Ω∪∂Ω, where each 2-cell is either a triangle or a quadrilateral. From these data and a conductance function we construct a canonical pair (S,f) where S is a special type of a (possibly immersed) genus (m-1) singular flat surface, tiled by rectangles and f is an energy preserving mapping from T(1) onto S. In Hersonsky (in press) [16] the solution of a Dirichlet problem defined on T(0) was utilized, in this paper we employ the solution of a mixed Dirichlet-Neumann problem.

Original languageEnglish
Pages (from-to)329-347
Number of pages19
JournalDifferential Geometry and its Applications
Volume29
Issue number3
DOIs
StatePublished - 1 Jun 2011
Externally publishedYes

Keywords

  • Flat surfaces with conical singularities
  • Harmonic functions on graphs
  • Planar networks
  • Primary
  • Secondary

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics

Fingerprint

Dive into the research topics of 'Boundary value problems on planar graphs and flat surfaces with integer cone singularities, II: The mixed Dirichlet-Neumann problem'. Together they form a unique fingerprint.

Cite this