an:04038591
Zbl 0637.47035
Nugari, Rita
Continuity and differentiability properties of the Nemitskii operator in H??lder spaces
EN
Glasg. Math. J. 30, No. 1, 59-65 (1988).
00166865
1988
j
47J05 46G05 47H99 46E40 35J65 26A16
Nemitskij operator in H??lder spaces; nonlinear superposition operator; locally Lipschitz; continuously differentiable; vector valued functions; nonlinear elliptic boundary value problems
Given a bounded domain \(\Omega\) in \({\mathbb{R}}^ n\), the author gives (sufficient) conditions for a real function f on \({\bar \Omega}\times {\mathbb{R}}\) under which the nonlinear superposition operator \(Fu(x)=f(x,u(x))\) acts in the H??lder space \(C^{\alpha}({\bar \Omega},{\mathbb{R}})\) and is continuous, locally Lipschitz, or continuously differentiable. In the last section, these results are generalized to vector valued functions, including an application to nonlinear elliptic boundary value problems.
J.Appell