Evolution problems related to a certain class of convex functionals on the Lebesgue space L₂((0,1)) are considered. The functionals are specified as the integrals of the composition of the classical derivative of the argument and a decreasing convex function. The functionals under examination are proved to be lower semicontinuous; an explicit form of their subdifferentials is found; and it is shown that the domains of the subdifferentials contain discontinuous functions. In particular, an evolution equation related to the functionals under examination has discontinuous solutions.
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M. S. Romanov (2026) studied this question.
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