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We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising, for instance, in finance and economics. The underlying process is a strong solution of a one-dimensional, time-homogeneous stochastic differential equation (SDE). The proof relies on both analytic and probabilistic arguments and is based on a contradiction scheme inspired by the maximum principle in partial differential equations theory. Mild, local regularity of the coefficients of the SDE and smoothness of the gain function locally at the boundary are required. [ABSTRACT FROM AUTHOR]

We establish a 1:1 correspondence between Poisson–Lie group actions on integrable Poisson manifolds and twisted multiplicative Hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson–Lie group G on a Poisson manifold M, we find an explicit description of the lifted Hamiltonian action on the symplectic groupoid Σ( M). We give applications of these results to the integration of Poisson quotients M/ G, Lu–Weinstein quotients μ−1( e)/ G and Poisson homogeneous spaces G/ H. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called Caplygin systems. [ABSTRACT FROM AUTHOR]