THE SUBDIFFERENTIAL OF THE FUNCTIONAL IN TWO-DIMENSIONAL ABSOLUTELY CONTINUOUS FUNCTIONS

Abstract

The subdifferential of a functional of a special form in the space of continuous functions, in the space of absolutely continuous and two-dimensional absolutely continuous functions in the work studies. The work studies the subdifferential of the integral and terminal functionals on the space of two-dimensional absolutely continuous functions. Two different norms are considered in the space of ab
solutely continuous and two-dimensional absolutely continuous functions, showing that the subdifferentials in these norms coincide. Using these equalities, subdifferentials of integral functionals are studied. Next, an analogue of the lemma of the classical calculus of variations for two-dimensional absolutely continuous functions is proved. Using this lemma, we study the subdifferential of the terminal functional in the class of two-dimensional absolutely continuous functions.