Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations

@misc{wang2026asymptotically,
  title = {{Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations}},
  author = {Jiangwen Wang and Yini Zhang and Feida Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34855},
  eprint = {2609.34855},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34855},
}

TY  - UNPB
TI  - Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations
AU  - Jiangwen Wang
AU  - Yini Zhang
AU  - Feida Jiang
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34855
UR  - https://arxiv.org/abs/2609.34855
AB  - We study bounded viscosity solutions of the degenerate or singular parabolic equation u_t−|Du|^γΔ_p^Nu=f in Q_1, where Δ_p^Nu := Δu+(p−2) ⟨ D^2uDu/|Du|, Du/|Du| ⟩, −1<γ<∞, 1<p<∞, and f∈ C^0(Q_1)∩ L^∞(Q_1). Given any prescribed α∈(0,1), we prove that there exists ε=ε(n,α)>0 such that |p−2|+|γ|≤ε Longrightarrow u∈ C_loc^1+α,(1+α)/2(Q_1). In particular, the spatial gradient Hölder exponent can be chosen arbitrarily close to $ 1 $ as (p,γ)→(2,0). This extends the result of Andrade and Santos (Calc. Var. Partial Differential Equations \textbf{61}, Paper No. 196, 2022) for γ=0 to the joint regime (p,γ)→(2,0) and answers affirmatively the question raised in Remark~1.1 therein.
ER  -