The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rn and metric spaces
2015 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 40, 89-108 p.Article in journal (Refereed) Published
The obstacle problem associated with p-harmonic functions is extended to unbounded open sets, whose complement has positive capacity, in the setting of a proper metric measure space supporting a (p,p)-Poincaré inequality, 1<p<∞, and the existence of a unique solution is proved. Furthermore, if the measure is doubling, then it is shown that a continuous obstacle implies that the solution is continuous, and moreover p-harmonic in the set where it does not touch the obstacle. This includes, as a special case, the solution of the Dirichlet problem for p-harmonic functions with Sobolev type boundary data.
Place, publisher, year, edition, pages
2015. Vol. 40, 89-108 p.
Dirichlet problem, Dirichlet space, doubling measure, metric space, minimal p-weak upper gradient, Newtonian space, nonlinear, obstacle problem, p-harmonic, Poincaré inequality, potential theory, upper gradient
IdentifiersURN: urn:nbn:se:liu:diva-114769DOI: 10.5186/aasfm.2015.4005ISI: 000349659000005OAI: oai:DiVA.org:liu-114769DiVA: diva2:792368