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I am trying to estimate, in either direction, the following integral:

$\int_{B} a^{i,j} X_j D_ig dx$ . We are integrating over a unit ball, $B$, and $[a^{i,j}]$ is positive.

I have tried to use ellipticity, but it didn't work. I was wondering if some one can show me: a. How to use ellipticity to estimate the integral, or b. Is there any other inequality that can be useful to estimating the integral. Thanks in advance.

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    Can you write down the form at least of the estimate that you are hoping to prove?2011-02-11
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    Thank you so much guys! Very helpful.2011-02-13
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    @Praire: please do not use answers to comment.2011-02-13

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