Sharp Hölder regularity for the inhomogeneous Trudinger’s equation

Nicolau M.L. Diehl, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We show that locally bounded solutions of the inhomogeneous Trudinger’s equation ∂t (|u|p−2u) − div|∇u|p−2∇u = f ∈ Lq,r, p > 2, are locally Hölder continuous with exponent γ = min { α−0(pqq−(pn−)r1)−rpq} , where α0 denotes the optimal Hölder exponent for solutions of the homogeneous case. We provide a streamlined proof, using the full power of the homogeneity in the equation to develop the regularity analysis in the p-parabolic geometry, without any need of intrinsic scaling, as anticipated by Trudinger. The main difficulty in the proof is to overcome the lack of a translation invariance property.
Original languageEnglish (US)
Pages (from-to)7054-7066
Number of pages13
Issue number12
StatePublished - Nov 9 2020
Externally publishedYes

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Generated from Scopus record by KAUST IRTS on 2023-02-15


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