A note on the point-wise behaviour of bounded solutions for a non-standard elliptic operator
| Autor: | Baldelli, Laura, Ciani, Simone, Skrypnik, Igor I., Vespri, Vincenzo |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this brief note we discuss local H\"older continuity for solutions to anisotropic elliptic equations of the type $ \sum_{i=1}^s \partial_{ii} u+ \sum_{i=s+1}^N \partial_i \bigg(A_i(x,u,\nabla u) \bigg) =0,$ for $x \in \Omega \subset \subset \mathbb{R}^N$ and $1\leq s \leq N-1$, where each operator $A_i$ behaves directionally as the singular $p$-Laplacian, $1< p < 2$ and the supercritical condition $p+(N-s)(p-2)>0$ holds true. We show that the Harnack inequality can be proved without the continuity of solutions and that in turn this implies H\"older continuity of solutions. Comment: 17 pages |
| Databáze: | arXiv |
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