Editing Maximum principle (section)

===Non-applicability of the strong maximum principle===
However, the above reasoning no longer applies if one considers the condition 
:<math>\sum_{i=1}^n\sum_{j=1}^n a_{ij}\frac{\partial^2u}{\partial x^i\,\partial x^j}+\sum_{i=1}^n b_i\frac{\partial u}{\partial x^i}\leq 0,</math>
since now the "balancing" condition, as evaluated at a hypothetical maximum point of {{mvar|u}}, only says that a weighted average of manifestly nonpositive quantities is nonpositive. This is trivially true, and so one cannot draw any nontrivial conclusion from it. This is reflected by any number of concrete examples, such as the fact that
:<math>\frac{\partial^2}{\partial x^2}\big({-x}^2-y^2\big)+\frac{\partial^2}{\partial y^2}\big({-x}^2-y^2\big)\leq 0,</math>
and on any open region containing the origin, the function {{math|−''x''<sup>2</sup>−''y''<sup>2</sup>}} certainly has a maximum.