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Differential inclusions for differential forms

Bandyopadhyay, Saugata ; Barroso, Ana ; Dacorogna, Bernard ; Matias, José

In: Calculus of Variations and Partial Differential Equations, 2007, vol. 28, no. 4, p. 449-469

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    Title
    • Differential inclusions for differential forms
    Author
    • Bandyopadhyay, Saugata. Section de Mathématiques, EPFL, Station 8, 1015, Lausanne, Switzerland
    • Barroso, Ana. CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal
    • Dacorogna, Bernard. Section de Mathématiques, EPFL, Station 8, 1015, Lausanne, Switzerland
    • Matias, José. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1, 1049-001, Lisboa, Portugal
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Calculus of Variations and Partial Differential Equations, 2007, vol. 28, no. 4, p. 449-469. Springer-Verlag
    Other Version
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:315387
    Summary
    We study necessary and sufficient conditions for the existence of solutions in $$W^{1,\infty}_0 (\Omega; \Lambda^{k}(\mathbb{R}^n))$$ of the problem $${\rm d}\omega (x)\in E,\quad \text{a.e. in }\Omega$$ where $$E\subseteq\Lambda^{k+1}(\mathbb{R}^{n})$$ is a given set. Special attention is given to the case of the curl (i.e. k = 1), particularly in dimension 3. Some applications to the calculus of variations are also stated