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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.

Global analysis (Mathematics). --- Mathematical optimization. --- Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Boundary value problems. --- Boundary conditions (Differential equations) --- Differential equations --- Mathematical physics --- Initial value problems --- Mathematical analysis. --- Analysis (Mathematics). --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- 517.1 Mathematical analysis