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.

Show me the PDF file (228 KB), TEX file, and other files for this article.

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

Return to the EJDE web page