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Mathematics in Engineering

2021, Volume 3, Issue 6:1-15. doi: 10.3934/mine.2021046
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Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group

  • 1.
    Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri 3, 56126 Pisa (PI), Italy
  • 2.
    Università degli Studi di Trento, via Sommarive 14, 38123 Povo (TN), Italy
  • Received: 03 July 2020 Accepted: 06 November 2020 Published: 13 November 2020

  • We examine the geometry of the level sets of particular horizontally p-harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the level sets of the p-capacitary potential of a bounded annulus in the Heisenberg group are strictly starshaped.

    Citation: Mattia Fogagnolo, Andrea Pinamonti. Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group[J]. Mathematics in Engineering, 2021, 3(6): 1-15. doi: 10.3934/mine.2021046

    Related Papers:

  • We examine the geometry of the level sets of particular horizontally p-harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the level sets of the p-capacitary potential of a bounded annulus in the Heisenberg group are strictly starshaped.


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