Semiconcavity is a natural generalization of concavity that retains most
of the good properties known in convex analysis, but arises in a wider
range of applications. This volume details the theory of semiconcave
functions, and of the role they play in optimal control and
Hamilton-Jacobi equations. The first part covers the general theory,
encompassing all key results and illustrating them with significant
examples. The latter part is devoted to applications concerning the
Bolza problem in the calculus of variations and optimal exit time
problems for nonlinear control systems.