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.