2023-03-30T07:09:17Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/825422022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Continuity of derivatives of a convex solution to a perturbed one-Laplace equation by p-LaplacianGiga, YoshikazuTsubouchi, Shuntaroopen access410We consider a one-Laplace equation perturbed by p-Laplacian with 1 < p < ∞. We prove that a weak solution is continuously differentiable (C1) if it is convex. Note that similar result fails to hold for the unperturbed one-Laplace equation. The main difficulty is to show C1-regularity of the solution at the boundary of a facet where the gradient of the solution vanishes. For this purpose we blow-up the solution and prove that its limit is a constant function by establishing a Liouville-type result, which is proved by showing a strong maximum principle. Our argument is rather elementary since we assume that the solution is convex. A few generalization is also discussed.Department of Mathematics, Hokkaido University2021-08-30engdepartmental bulletin paperVoRhttps://doi.org/10.14943/99357http://hdl.handle.net/2115/8254210.14943/99357Hokkaido University Preprint Series in Mathematics1137129https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/82542/1/ConDerConvex.pdfapplication/pdf211.72 KB2021-08-30