scholarly journals Boundary regularity of harmonic maps to nonpositively curved metric spaces

1994 ◽  
Vol 2 (1) ◽  
pp. 139-153 ◽  
Author(s):  
Tomasz Serbinowski
Keyword(s):  
Metric Spaces ◽  
Harmonic Maps ◽  
Boundary Regularity ◽  
Nonpositively Curved

scholarly journals Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 179-196
Author(s):  
Anders Björn ◽  
Daniel Hansevi
Keyword(s):  
Harmonic Functions ◽  
Obstacle Problem ◽  
Metric Spaces ◽  
Local Property ◽  
Boundary Regularity ◽  
Obstacle Problems ◽  
Regular Boundary ◽  
Complete Metric Spaces ◽  
Regularity Results

Abstract The theory of boundary regularity for p-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. The barrier classification of regular boundary points is established, and it is shown that regularity is a local property of the boundary. We also obtain boundary regularity results for solutions of the obstacle problem on open sets, and characterize regularity further in several other ways.

scholarly journals UNIQUENESS THEOREMS FOR HARMONIC MAPS INTO METRIC SPACES

2002 ◽  
Vol 04 (04) ◽  
pp. 725-750 ◽  
Author(s):  
CHIKAKO MESE
Keyword(s):  
Riemannian Manifolds ◽  
Metric Space ◽  
Metric Spaces ◽  
Harmonic Maps ◽  
Uniqueness Theorems ◽  
Singular Spaces ◽  
Domain Space ◽  
Recent Developments

Recent developments extend much of the known theory of classical harmonic maps between smooth Riemannian manifolds to the case when the target is a metric space of curvature bounded from above. In particular, the existence and regularity theorems for harmonic maps into these singular spaces have been successfully generalized. Furthermore, the uniqueness of harmonic maps is known when the domain has a boundary (with a smallness of image condition if the target curvature is bounded from above by a positive number). In this paper, we will address the question of uniqueness when the domain space is without a boundary in two cases: one, when the curvature of the target is strictly negative and two, for a map between surfaces with nonpositive target curvature.

scholarly journals Boundary regularity and the Dirichlet problem for harmonic maps

1983 ◽  
Vol 18 (2) ◽  
pp. 253-268 ◽  
Author(s):  
Richard Schoen ◽  
Karen Uhlenbeck
Keyword(s):  
Dirichlet Problem ◽  
Harmonic Maps ◽  
Boundary Regularity
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