# How do i show the following bilinear operator is continuous and coercieve ?

We have $Lu=-\sum_{i,j=1}^n (a^{ij}u_{x_i})_{x_j}+cu$ , I want to show that there exists a constant $\mu \ge0$ such that Bilinear $B$ satisfies Lax milgram hypothesis for every $c(x) \ge 0$. I am basically not able to show that it is continuous and it is coercieve . How can i do it ? A binilinear form is continuous if $|B[u,v]\le\alpha||u|| ||v|||$ and coercive if $B[u,u]\ge\beta||u||^2$ , where $\beta, \alpha>0$ This is a problem from Evans chapter 6. Thanks a lot .

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Given vectors $u,v$ - do you know how $B[u,v]$ looks like? – Ilya Jun 12 '12 at 10:40
@Ilya : Does it look like $\sum ||c^{i,j}||_{L^\infty} \int |Du||Dv|dx + ||c|| \int |u||v| dx$ – Theorem Jun 12 '12 at 10:46
Well, I think you should take a look on formula (8) in that book (p. 296). Also, what are $c^{i,j}$? What is $\mu$? – Ilya Jun 12 '12 at 11:17