On the Continuity of the Nemitsky Operator Induced by a Lipschitz Continuous Map

DOI10.2307/2048570zbMath0752.46016OpenAlexW4230086089MaRDI QIDQ3971077

Roberta Musina

Publication date: 25 June 1992

Full work available at URL: https://doi.org/10.2307/2048570

zbMATH Keywords

Sobolev spacesuperposition operatorLipschitz continuous functionNemitsky operator

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30)

Related Items (2)

Differentiability properties of the autonomous composition operator in Sobolev spaces ⋮ On the regularity of weak solutions to \(H\)-system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A continuity theorem for operators from \(W^{1,q}(\Omega)\) into \(L^ r(\Omega)\)
• Every superposition operator mapping one Sobolev space into another is continuous
• Isoperimetric inequalities and the problem of Plateau
• Absolute continuity on tracks and mappings of Sobolev spaces
• An Approach to the Thin Obstacle Problem foŕ Variational Functionals Depending on Vector Valued Functions
• A General Chain Rule for Distributional Derivatives

This page was built for publication: On the Continuity of the Nemitsky Operator Induced by a Lipschitz Continuous Map