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

Bögelein V, Duzaar F, Liao N, Schätzler L (2023)


Publication Language: English

Publication Type: Journal article

Publication year: 2023

Journal

Book Volume: 39

Pages Range: 1005-1037

Journal Issue: 3

DOI: 10.4171/RMI/1342

Abstract

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 (|u|q-1u) - Δpu = 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 initial-boundary value problems of Dirichlet and Neumann type.

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APA:

Bögelein, V., Duzaar, F., Liao, N., & Schätzler, L. (2023). On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II. Revista Matematica Iberoamericana, 39(3), 1005-1037. https://doi.org/10.4171/RMI/1342

MLA:

Bögelein, Verena, et al. "On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II." Revista Matematica Iberoamericana 39.3 (2023): 1005-1037.

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