scholarly journals Holomorphic mappings between domains with low boundary regularity

2021 ◽  
Vol 85 (3) ◽  
Author(s):  
Alexandre Borisovich Sukhov
Keyword(s):  
Boundary Regularity ◽  
Holomorphic Mappings

Boundary regularity of proper holomorphic mappings

1982 ◽  
Vol 67 (3) ◽  
pp. 363-384 ◽  
Author(s):  
Klas Diederich ◽  
John Eric Fornaess
Keyword(s):  
Boundary Regularity ◽  
Holomorphic Mappings ◽  
Proper Holomorphic Mappings

Local boundary regularity of holomorphic mappings

1980 ◽  
Vol 33 (3) ◽  
pp. 305-338 ◽  
Author(s):  
L. Nirenberg ◽  
S. Webster ◽  
P. Yang
Keyword(s):  
Boundary Regularity ◽  
Holomorphic Mappings ◽  
Local Boundary

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.

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