Obstacle problems — an important category of free boundary problems in the area of mathematical physics — involve the applicability of elliptic variational inequalities. This research monograph features a three-part treatment of the subject: introducing mathematical physics, discussing unilateral elliptic variational inequalities, and exploring this material in terms of its applications in mechanics and physics.
Part I begins with a look at the obstacle problem that features some free boundary problems and mathematical tools. Part II examines variational inequalities in Hilbert spaces, the smoothness of the variational solution, the coincidence set and the free boundary, and unilateral plateau problems. The final part, which focuses on applications, explores applied obstacle problems as well as dam and Stefan type problems. A substantial bibliography enhances the text.
For advanced undergraduates and graduate students in mathematics and engineering.