In the middle of a proof I encountered this type of expression:
$$\int_D Af^2+\int_{\partial D} Bf^2$$
where $D$ is a domain and $A$ and $B$ are not constants. I would like to find a lower bound of the form:
$$M\int_Df^2$$
for some $M$, but I am not sure whether this is possible in general. I thought of ignoring the second term and using Cauchy-Schwarz inequality on the first, but this gives me an upper instead of a lower bound. Any advice?