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Hokkaido University Preprint Series in Mathematics >
Continuity of derivatives of a convex solution to a perturbed one-Laplace equation by p-Laplacian
| Title: | Continuity of derivatives of a convex solution to a perturbed one-Laplace equation by p-Laplacian |
| Authors: | Giga, Yoshikazu Browse this author | | Tsubouchi, Shuntaro Browse this author |
| Issue Date: | 30-Aug-2021 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1137 |
| Start Page: | 1 |
| End Page: | 29 |
| Abstract: | We 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/82542 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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