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2016-01-26 Nonlinear Seminar

Piotr Maćkowiak
Continuity of the non-autonomous superposition operator and around

We shall present an example of a function $$ f:[0,1]\times\mathbb R\to \mathbb R $$ which is lipschitzian and such that the (non-autonomous) superposition operator it generates is not continuous (as a mapping from $$ BV $$ to $$ BV $$). We shall show necessary and sufficient conditions for a non-autonomous superposition operator to be continuous (in $$ BV $$). We shall also prove some results for $$ C^1 $$-class generators.