A continuity theorem for operators from \(W^{1,q}(\Omega)\) into \(L^ r(\Omega)\)

DOI10.1016/0022-1236(84)90040-5zbMath0548.46027OpenAlexW2053537707MaRDI QIDQ799903

Antonio Leaci, Giusseppe Buttazzo

Publication date: 1984

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(84)90040-5

zbMATH Keywords

Sobolev spacecontinuitysuperposition operators

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Methods involving semicontinuity and convergence; relaxation (49J45) Linear operators on function spaces (general) (47B38) Representation and superposition of functions (26B40) Nonlinear operators and their properties (47H99)

Related Items (2)

On the Continuity of the Nemitsky Operator Induced by a Lipschitz Continuous Map ⋮ Relaxation results for a class of variational integrals

Cites Work

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• Every superposition operator mapping one Sobolev space into another is continuous
• A characterization of first order nonlinear partial differential operators on Sobolev spaces
• Absolute continuity on tracks and mappings of Sobolev spaces

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