Geodesic
Approximations by regular sets and Wiener solutions in metric spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 343-355 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $X$ be a complete metric space equipped with a doubling Borel measure supporting a weak Poincaré inequality. We show that open subsets of $X$ can be approximated by regular sets. This has applications in nonlinear potential theory on metric spaces. In particular it makes it possible to define Wiener solutions of the Dirichlet problem for $p$-harmonic functions and to show that they coincide with three other notions of generalized solutions.
Let $X$ be a complete metric space equipped with a doubling Borel measure supporting a weak Poincaré inequality. We show that open subsets of $X$ can be approximated by regular sets. This has applications in nonlinear potential theory on metric spaces. In particular it makes it possible to define Wiener solutions of the Dirichlet problem for $p$-harmonic functions and to show that they coincide with three other notions of generalized solutions.
Classification : 31C45, 31D05, 35J70, 49J27
Keywords: axiomatic potential theory; capacity; corkscrew; Dirichlet problem; doubling; metric space; nonlinear; $p$-harmonic; Poincaré inequality; quasiharmonic; quasisuperharmonic; quasiminimizer; quasisuperminimizer; regular set; Wiener solution 
@article{CMUC_2007_48_2_a14,
     author = {Bj\"orn, Anders and Bj\"orn, Jana},
     title = {Approximations by regular sets and {Wiener} solutions in metric spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {343--355},
     year = {2007},
     volume = {48},
     number = {2},
     mrnumber = {2338101},
     zbl = {1199.31024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2007_48_2_a14/}
}
TY  - JOUR
AU  - Björn, Anders
AU  - Björn, Jana
TI  - Approximations by regular sets and Wiener solutions in metric spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2007
SP  - 343
EP  - 355
VL  - 48
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_2007_48_2_a14/
LA  - en
ID  - CMUC_2007_48_2_a14
ER  - 
%0 Journal Article
%A Björn, Anders
%A Björn, Jana
%T Approximations by regular sets and Wiener solutions in metric spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 2007
%P 343-355
%V 48
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_2007_48_2_a14/
%G en
%F CMUC_2007_48_2_a14
Björn, Anders; Björn, Jana. Approximations by regular sets and Wiener solutions in metric spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 343-355. http://geodesic.mathdoc.fr/item/CMUC_2007_48_2_a14/