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**Nonlinear elliptic systems.**
*(English)*
Zbl 0912.35057

Summary: This is a survey article on nonlinear elliptic systems arising from multidimensional calculus of variations. It has been written on request of the Editorial Board of Jahresberichte der Deutschen Mathematiker Vereinigung on the occasion of the publication of their 100th volume. I should like to thank the colleagues of Jahresberichte and the German Mathematical Society for the great honour that has fallen to me with this invitation.

The paper does not aim at completeness but only at discussing a few selected topics mainly about the regularity theory for nonlinear elliptic systems following the paper by E. HĂ¶lder [Jahresber. Dtsch. Math.-Ver., 62, 34-52 (1959; Zbl 0086.30605)]. The choice of the topics obviously depends on the taste of the author, on his limited knowledge and on the intention of keeping the paper in reasonable size: I shall therefore apologize for the many relevant omissions.

The paper does not aim at completeness but only at discussing a few selected topics mainly about the regularity theory for nonlinear elliptic systems following the paper by E. HĂ¶lder [Jahresber. Dtsch. Math.-Ver., 62, 34-52 (1959; Zbl 0086.30605)]. The choice of the topics obviously depends on the taste of the author, on his limited knowledge and on the intention of keeping the paper in reasonable size: I shall therefore apologize for the many relevant omissions.

### MSC:

35J50 | Variational methods for elliptic systems |

35B65 | Smoothness and regularity of solutions to PDEs |

58E20 | Harmonic maps, etc. |

35J60 | Nonlinear elliptic equations |

49Q20 | Variational problems in a geometric measure-theoretic setting |

35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |