The dirichlet problem for harmonic functions from variable exponent smirnov classes in domains with piecewise smooth boundary

2010 ◽  
Vol 172 (3) ◽  
pp. 401-421 ◽  
Author(s):  
V. Kokilashvili ◽  
V. Paatashvili
Keyword(s):  
Dirichlet Problem ◽  
Harmonic Functions ◽  
Variable Exponent ◽  
Smooth Boundary ◽  
Piecewise Smooth ◽  
Piecewise Smooth Boundary ◽  
Smirnov Classes

Conditionally invariant measures for Anosov maps with small holes

1998 ◽  
Vol 18 (5) ◽  
pp. 1049-1073 ◽  
Author(s):  
N. CHERNOV ◽  
R. MARKARIAN ◽  
S. TROUBETZKOY
Keyword(s):  
Invariant Measure ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Smooth Boundary ◽  
Piecewise Smooth ◽  
Piecewise Smooth Boundary ◽  
Conditional Distributions ◽  
The Past ◽  
Set Of Points ◽  
Small Holes

We study Anosov diffeomorphisms on surfaces in which some small ‘holes’ are cut. The points that are mapped into those holes disappear and never return. We assume that the holes are arbitrary open domains with piecewise smooth boundary, and their sizes are small enough. The set of points whose trajectories never enter holes under the past iterations of the map is a Cantor-like union of unstable fibers. We establish the existence and uniqueness of a conditionally invariant measure on this set, whose conditional distributions on unstable fibers are smooth. This generalizes previous works by Pianigiani, Yorke, and others.

scholarly journals On the existence of strongly regular families of triangulations for domains with a piecewise smooth boundary

1999 ◽  
Vol 44 (1) ◽  
pp. 33-42 ◽  
Author(s):  
Sergey Korotov ◽  
Michal Křížek ◽  
Pekka Neittaanmäki
Keyword(s):  
Smooth Boundary ◽  
Piecewise Smooth ◽  
Piecewise Smooth Boundary ◽  
Strongly Regular
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