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An elliptic operator $L$ is called uniformly elliptic if $a^{ij}(x)\xi _i\xi_j \ge \theta|\xi|^2$. What does this notation mean? All I can find about it is that it is some kind of summation notation or something. Can anyone explain me what it is?

Thank you very much.

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    @did : Sir , i didn't understand what u meant by leaving the question open .2012-07-15

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$\forall \xi=(\xi_i)_i\qquad\sum\limits_{i,j}a^{ij}(x)\xi_i\xi_j \geqslant \theta\cdot|\xi|^2=\theta\cdot\sum\limits_i\xi_i^2$

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    In other words, the matrix $A - \theta I$ is positive semidefinite, where $A_{ij} = a^{ij}(x)$. For the operator to be uniformly elliptic on domain $\Omega$, you want there to be some \theta > 0 that makes this true for all $x \in \Omega$.2012-07-10