scholarly journals Some remarks on the Dirichlet problem on infinite trees

2019 ◽  
Vol 6 (1) ◽  
pp. 20-32
Author(s):  
Nikolaos Chalmoukis ◽  
Matteo Levi
Keyword(s):  
Dirichlet Problem ◽  
Rooted Trees ◽  
Continuous Data ◽  
Uniqueness Results ◽  
Infinite Trees ◽  
Zero Capacity

Abstract We consider the Dirichlet problem on in_nite and locally _nite rooted trees, andwe prove that the set of irregular points for continuous data has zero capacity. We also give some uniqueness results for solutions in Sobolev W1,p of the tree.

scholarly journals Dirichlet Problem for Maximal Graphs of Higher Codimension

2020 ◽  
Author(s):  
Yang Li
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
General Existence

Abstract We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian-type ambient spaces and obtain general existence and uniqueness results that apply to any codimension.

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