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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.


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