The analysis of the Neumann and the oblique derivative problem: the theoryof regularization and its stochastic version

Following a detailed analysis of the weak solution of Neumann and oblique d erivative problems [Rozanov and Sanso (1999). The analysis of the Neumann a nd the oblique derivative problem. Weak theory], here the so-called regular ization theory is presented. The result, which is already known in mathemat ical literature, is obtained via a so-called Ladyzenskaya identity, which i s a very interesting tool in itself. The analysis of the stochastic version s of the same problems is tackled and solved. In so doing, the question of the equivalence between different definitions of generalized random fields is also analyzed.