This book is concerned with several elliptic and parabolic obstacle-type problems with a focus
on the cases where the free and fixed boundaries meet. The results presented complement those
found in existing books in the subject which mainly treat regularity properties away from the
fixed boundary. The topics include optimal regularity analysis of global solutions tangential
touch of the free and fixed boundaries as well as Lipschitz- and $C^1$-regularity of the free
boundary. Special attention is given to local versions of various monotonicity formulas. The
intended audience includes research mathematicians and advanced graduate students interested in
problems with free boundaries.
