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Zbl 0913.35026
D'Ottavio, Anna; Leonetti, Francesco; Musciano, Chiara
Maximum principle for vector-valued mappings minimizing variational integrals. (English)
[J] Atti Semin. Mat. Fis. Univ. Modena 46, Suppl., 677-683 (1998). ISSN 0041-8986

Summary: We prove a maximum principle for (possibly) vector-valued mappings $u$ minimizing integral functionals depending on minors taken from the Jacobian matrix $Du$. Such a maximum principle allows us to apply a theorem by D'Ottavio about the higher integrability of the gradient of bounded minimizers of some anisotropic integrals.

MSC 2000:: *35B50 Maximum principles (PDE)
49N60 Regularity of solutions in the calculus of variations
35J60 Nonlinear elliptic equations

Keywords: integrability of the gradient; anisotropic integrals

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