On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II

• Verena Bögelein ^[1] ; Frank Duzaar ^[2] ; Naian Liao ^[1] ; Leah Schätzler ^[1]
  1. [1] Paris-Lodron-Universität Salzburg, Austria
  2. [2] Universität Erlangen-Nürnberg, Germany
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 3, 2023, págs. 1005-1037
• Idioma: inglés
• DOI: 10.4171/RMI/1342
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• Resumen

  • We demonstrate two proofs for the local Hölder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is @t.juj q1u/ pu D 0; p > 2; 0 < q < p 1: The first proof takes advantage of the expansion of positivity for the degenerate, parabolic p-Laplacian, thus simplifying the argument; the second proof relies solely on the energy estimates for doubly nonlinear parabolic equations. After proper adaptations of the interior arguments, we also obtain the boundary regularity for initialboundary value problems of Dirichlet and Neumann type