A Multi-dimensional Optimal Harvesting Problem with Measure Valued Solutions

The paper is concerned with the optimal harvesting of a marine resource, described by an elliptic equation with Neumann boundary conditions and a nonlinear source term. Since the cost function has linear growth, an optimal solution is found within the class of measure-valued control strategies. The paper also provides results on the existence and uniqueness of strictly positive solutions to the elliptic equation, and an averaging inequality valid for subharmonic functions with Neumann boundary data