References
- Björn A , Björn J , Shanmugalingam N . The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities. J Differ Equ. 2015;259:3078–3114.
- Björn A , Björn J , Sjödin T . The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications. Rev Mat Iberoam. Forthcoming.
- Björn A , Björn J , Shanmugalingam N . The Dirichlet problem for p-harmonic functions on metric spaces. J Reine Angew Math. 2003;556:173–203.
- Mazurkiewicz S . Sur une classification de points situés un sur continu arbitraire [O pewnej klasyfikacyi punkt’ow leż̧cych na kontynuach dowolnych]. CR Soc Sci Lett Varsovie. 1916;9(5):428–442 (Polish with French summary at the end).
- Björn A , Björn J , Shanmugalingam N . The Mazurkiewicz distance and sets which are finitely connected at the boundary. J Geom Anal. 2016;26:873–897.
- Maz’ya VG . On the continuity at a boundary point of solutions of quasi-linear elliptic equations Vestnik Leningrad Univ Mat Mekh Astronom [Vestnik Leningrad Univ Math]. 1970;25(13):42–55; 1976;3:225--242. Russian.
- Heinonen J , Kilpeläinen T , Martio O . Nonlinear potential theory of degenerate elliptic equations. 2nd ed. Mineola (NY): Dover; 2006.
- Kilpeläinen T , Malý J . The Wiener test and potential estimates for quasilinear elliptic equations. Acta Math. 1994;172:137–161.
- Lindqvist P , Martio O . Two theorems of N. Wiener for solutions of quasilinear elliptic equations. Acta Math. 1985;155:153–171.
- Mikkonen P . On the Wolff potential and quasilinear elliptic equations involving measures. Ann Acad Sci Fenn Math Diss. 1996;104.
- Björn J . Wiener criterion for Cheeger p-harmonic functions on metric spaces. In: Aikawa H , Kumagai T , Mizuta Y , Suzuki N , editors. Potential theory in Matsue. Vol. 44, Advanced studies in pure mathematics. Tokyo: Mathematical Society of Japan; 2006. pp. 103–115.
- Björn J , MacManus P , Shanmugalingam N . Fat sets and pointwise boundary estimates for p-harmonic functions in metric spaces. J Anal Math. 2001;85:339–369.
- Björn J . Fine continuity on metric spaces. Manuscripta Math. 2008;125:369–381.
- Björn J . Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations. Calc Var Partial Differ Equ. 2009;35:481–496.
- Hedberg LI . Non-linear potentials and approximation in the mean by analytic functions. Math Z. 1972;129:299–319.
- Hedberg LI , Wolff TH . Thin sets in nonlinear potential theory. Ann Inst Fourier Grenoble. 1983;33(4):161–187.
- Kilpeläinen T . Potential theory for supersolutions of degenerate elliptic equations. Indiana Univ Math J. 1989;38:253–275.
- Vodop’yanov SK . Potential theory on homogeneous groups. Mat Sb [Math USSR Sb]. 1989;180:57–77; 1990;66:59--81. Russian.
- Markina IG , Vodop’yanov SK . Fundamentals of the nonlinear potential theory for subelliptic equations II. In: Reshetnyak, YuG, Vodop’yanov SK, editors. Sobolev spaces and related problems of analysis, Trudy Inst Mat. 31:123--160; Izdat Ross Akad Nauk Sib Otd Inst Mat [Siberian Adv Math], Novosibirsk, 1996; 1997;7(2):18-63. Russian.
- Björn A , Björn J , Latvala V . The Cartan, Choquet and Kellogg properties for the p-fine topology on metric spaces. J Anal Math. Forthcoming.
- Björn A . Weak barriers in nonlinear potential theory. Potential Anal. 2007;27:381–387.
- Björn A . A regularity classification of boundary points for p-harmonic functions and quasiminimizers. J Math Anal Appl. 2008;338:39–47.
- Björn A . p-harmonic functions with boundary data having jump discontinuities and Baernstein’s problem. J Differ Equ. 2010;249:1–36.
- Björn A . Cluster sets for Sobolev functions and quasiminimizers. J Anal Math. 2010;112:49–77.
- Björn A . The Dirichlet problem for p-harmonic functions on the topologist’s comb. Math Z. 2015;279:389–405.
- Björn A , Björn J . Boundary regularity for p-harmonic functions and solutions of the obstacle problem. J Math Soc Jpn. 2006;58:1211–1232.
- Björn A , Björn J . Approximations by regular sets and Wiener solutions in metric spaces. Comment Math Univ Carolin. 2007;48:343–355.
- Granlund S , Lindqvist P , Martio O . Note on the PWB-method in the nonlinear case. Pacific J Math. 1986;125:381–395.
- Kilpeläinen T , Lindqvist P . Nonlinear ground states in irregular domains. Indiana Univ Math J. 2000;49:325–331.
- Björn A , Björn J . Nonlinear potential theory on metric spaces. EMS tracts in mathematics. Vol. 17. Zürich: European Mathematical Society; 2011.
- Heinonen J , Koskela P , Shanmugalingam N , et al . Sobolev spaces on metric measure spaces. New mathematical monographs. Vol. 27. Cambridge: Cambridge University Press; 2015.
- Koskela P , MacManus P . Quasiconformal mappings and Sobolev spaces. Stud Math. 1998;131:1–17.
- Heinonen J , Koskela P . Quasiconformal maps in metric spaces with controlled geometry. Acta Math. 1998;181:1–61.
- Shanmugalingam N . Harmonic functions on metric spaces. Illinois J Math. 2001;45:1021–1050.
- Shanmugalingam N . Newtonian spaces: an extension of Sobolev spaces to metric measure spaces. Rev Mat Iberoam. 2000;16:243–279.
- Karmazin AP . Quasiisometries, the theory of prime ends and metric structures on domains. Izdat Surgut Surgut. 2008. Russian.
- Kilpeläinen T , Malý J . Generalized Dirichlet problem in nonlinear potential theory. Manuscripta Math. 1989;66:25–44.
- Pedersen GK . Analysis now. Graduate texts in mathematics. Vol. 118. New York (NY): Springer; 1989.
- Björn A . Characterizations of p-superharmonic functions on metric spaces. Stud Math. 2005;169:45–62.
- Kinnunen J , Martio O . Nonlinear potential theory on metric spaces. Illinois J Math. 2002;46:857–883.
- Björn A , Björn J , Shanmugalingam N . The Perron method for p-harmonic functions. J Differ Equ. 2003;195:398–429.
- Björn A . A weak Kellogg property for quasiminimizers. Comment Math Helv. 2006;81:809–825.
- Björn A , Björn J , Mäkäläinen T , et al . Nonlinear balayage on metric spaces. Nonlinear Anal. 2009;71:2153–2171.