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Large solutions for biharmonic maps in four dimensions

Angelsberg, Gilles

In: Calculus of Variations and Partial Differential Equations, 2007, vol. 30, no. 4, p. 417-447

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    Title
    • Large solutions for biharmonic maps in four dimensions
    Author
    • Angelsberg, Gilles. Departement für Mathematik, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Calculus of Variations and Partial Differential Equations, 2007, vol. 30, no. 4, p. 417-447. Springer-Verlag
    Other Version
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:321788
    Summary
    We seek critical points of the Hessian energy functional $$E_\Omega(u)\!=\!\int_\Omega\vert\Delta u\vert^2dx$$ , where $$\Omega={\mathbb R}^4$$ or Ω is the unit disk $$B$$ in $${\mathbb R}^4$$ and u : Ω → S 4. We show that $$E_{{\mathbb R}^4}$$ has a critical point which is not homotopic to the constant map. Moreover, we prove that, for certain prescribed boundary data on ∂B, E B achieves its infimum in at least two distinct homotopy classes of maps from B into S 4