Annales Academiĉ Scientiarum Fennicĉ
Mathematica
Volumen 34, 2009, 261-277
Linköping University, Department of Mathematics
SE-581 83 Linköping, Sweden; zofar 'at' mai.liu.se
Abstract. We study the double obstacle problem on a metric measure space equipped with a doubling measure and supporting a p-Poincaré inequality. We prove existence and uniqueness. We also prove the continuity of the solution of the double obstacle problem with continuous obstacles and show that the continuous solution is a minimizer in the open set where it does not touch the two obstacles. Moreover we consider the regular boundary points and show that the solution of the double obstacle problem on a regular open set with continuous obstacles is continuous up to the boundary. Regularity of boundary points is further characterized in some other ways using the solution of the double obstacle problem.
2000 Mathematics Subject Classification: Primary 49J40; Secondary 31C45.
Key words: Double obstacle problem, doubling measure, metric space, nonlinear, p-harmonic, Poincaré inequality, potential theory, regularity.
Reference to this article: Z. Farnana: The double obstacle problem on metric spaces. Ann. Acad. Sci. Fenn. Math. 34 (2009), 261-277.
Copyright © 2009 by Academia Scientiarum Fennica