Narrow Results

This paper deals with maximum principles for locally Lipschitz cost functionals, under constraints given by functional equations associated with pairs of closed range unbounded operators. The so called “range condition” introduced by the author, plays an essential role. Such abstract maximum principles have both a unifying effect in this area and applications to optimal control of some partial differential equations.

In this paper, a new theorem to the range conditions for the exponential Radon transform is established, their equivalent relationship theorem is proved with a new method.