  We investigate the statistics of encounters of a diffusing particle with
different subsets of the boundary of a confining domain. The encounters with
each subset are characterized by the boundary local time on that subset. We
extend a recently proposed approach to express the joint probability density of
the particle position and of its multiple boundary local times via a
multi-dimensional Laplace transform of the conventional propagator satisfying
the diffusion equation with mixed Robin boundary conditions. In the particular
cases of an interval, a circular annulus and a spherical shell, this
representation can be explicitly inverted to access the statistics of two
boundary local times. We provide the exact solutions and their probabilistic
interpretation for the case of an interval and sketch their derivation for two
other cases. We also obtain the distributions of various associated
first-passage times and discuss their applications.
