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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. Hölder [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.
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