  Uniqueness in the Calder\'on problem in dimension bigger than two was usually
studied under the assumption that conductivity has bounded gradient. For
conductivities with unbounded gradients uniqueness results have not been known
until recent years. The latest result due to Haberman basically relies on the
optimal $L^2$ restriction estimate for hypersurface which is known as the
Tomas-Stein restriction theorem. In the course of developments of the Fourier
restriction problem bilinear and multilinear generalizations of the (adjoint)
restriction estimates under suitable transversality condition between surfaces
have played important roles. Since such advanced machineries usually provide
strengthened estimates, it seems natural to attempt to utilize these estimates
to improve the known results. In this paper, we make use of the sharp bilinear
restriction estimates, which is due to Tao, and relax the regularity assumption
on conductivity. We also consider the inverse problem for the Schr\"odinger
operator with potentials contained in the Sobolev spaces of negative orders.
