An existence criterion for a smooth function under constraints
A problem of existence of a real function \(f\) such that \(f_1 \leq f \leq f_2\) for given \(f_1, f_2\) fulfilling some requirements on its derivative is studied. These requirements are: being locally Lipschitz with bounded gradient in the first part of the paper and having the first derivative bounded between two prescribed continuous functions in its second part. In both cases necessary and sufficient conditions for existence are found.
scientific article; zbMATH DE number 5319840
scientific article