A variant on Miranda-Talenti extimate

In this note we prove formula (1.1),which extends to functions in W^{2,2}(Ω) with zero normal derivative the analogous formula (1.2) by G. Talenti ([5]) on functions with zero trace. To prove (1.1) we use the technique introduced by C. Miranda in [3] and give a geometrical interpretation of his results (formula (2.17)).