Semiregular and strongly irregular boundary points for p-harmonic functions on unbounded sets in metric spaces

• Anders Björn ^[1] ; Daniel Hansevi ^[1]
  1. [1] Linköping University

     Linköping University

     Linköpings S:t Lars, Suecia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 2, 2022, págs. 253-270
• Idioma: inglés
• DOI: 10.1007/s13348-021-00317-6
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• Resumen

  • The trichotomy between regular, semiregular, and strongly irregular boundary points for p-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincaré inequality, 1 p \infty. We show that these are local properties. We also deduce several characterizations of semiregular points and strongly irregular points. In particular, semiregular points are characterized by means of capacity, p-harmonic measures, removability, and semibarriers.