Electron. J. Diff. Equ., Vol. 2015 (2015), No. 115, pp. 1-9.

Hopf maximum principle revisited

Jose C. Sabina de Lis

Abstract:
A weak version of Hopf maximum principle for elliptic equations in divergence form
$$ \sum_{i,j=1}^N\partial_i(a_{ij}(x)\partial_ju)=0 $$
with Holder continuous coefficients $a_{ij}$ was shown in [3], in the two-dimensional case. It was also pointed out that this result could be extended to any dimension. The objective of the present note is to provide a complete proof of this fact, and to cover operators more general than the one studied in [3].

Submitted December 29, 2014. Published April l28, 2015.
Math Subject Classifications: 35B50.
Key Words: Maximum principle.

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José C. Sabina de Lis
Departamento de Análisis Matemático and IUEA
Universidad de La Laguna
C. Astrofísico Francisco Sánchez s/n, 38203
La Laguna, Spain
email: josabina@ull.es

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