  We establish the convergence to the equilibrium for various linear
collisional kinetic equations (including linearized Boltzmann and Landau
equations) with physical local conservation laws in bounded domains with
general Maxwell boundary condition. Our proof consists in establishing an
hypocoercivity result for the associated operator, in other words, we exhibit a
convenient Hilbert norm for which the associated operator is coercive in the
orthogonal of the global conservation laws. Our approach allows us to treat
general domains with all type of boundary conditions in a unified framework. In
particular, our result includes the case of vanishing accommodation coefficient
and thus the specific case of the specular reflection boundary condition.
