Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control

We study the partial differential equation max{Lu - f, H(Du)}=0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Holder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution is Lipschitz continuous

On not becoming an agent of the state: church-related social welfare agency tactics in an era of government contracting

Identifies a range of possible tactics that are available to church-related agencies in their engagement with government. Abstract  United States, United Kingdom and Australian literature on the potential, and actual, impacts on not-for profit social welfare and human services agencies of contracting with government highlight the risk that such agencies will become ‘agents of the state’ without remainder, substantially losing their identity and character in the process. ‘ Church‐related’ agencies are now playing a significant role in the delivery of social welfare and human services in Australia, in a distinctive pattern of involvement with respect to the history and structure of service delivery, and the pattern of policy, political settlement and the constitutional basis when compared to that of both the United Kingdom and the United States. Against this background paper identifies a range of possible ‘tactics’ that are available to church-related agencies in their engagement with government. Using this framework the paper draws on interviews with a range of senior managers and staff and independent experts, from a purposive sample of church-related agencies and denominational coordinating bodies to explore the possibility that church-related agencies are exercising a degree of agency in their response to the contracting environment to resist, or deflect at least to some degree the impact of the sociological processes associated with the contracting environment. &nbsp