An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 23 (1996) no. 1, p. 57-67
@article{ASNSP_1996_4_23_1_57_0,
     author = {Hao, Wenge and Leonardi, Salvatore and Ne\v cas, Jind\v rich},
     title = {An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 23},
     number = {1},
     year = {1996},
     pages = {57-67},
     zbl = {0864.35031},
     mrnumber = {1401417},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1996_4_23_1_57_0}
}
Hao, Wenge; Leonardi, Salvatore; Nečas, Jindřich. An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 23 (1996) no. 1, pp. 57-67. http://www.numdam.org/item/ASNSP_1996_4_23_1_57_0/

[1] E. De Giorgi, Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. Un. Mat. Ital. 4 (1968), 135-137. | MR 227827 | Zbl 0155.17603

[2] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton University Press, Princeton, 1983. | MR 717034 | Zbl 0516.49003

[3] M. Giaquinta, Introduction to the regularity theory for nonlinear elliptci systems, Birkhäuser Verlag, Basel, Boston, Berlin 1993. | MR 1239172 | Zbl 0786.35001

[4] E. Giusti - M. Miranda, Un esempio di soluzione discontinua per un problema di minimo relativo ad un integrale regolare del calcolo delle variazioni, Boll. Un. Mat. Ital. 2 (1968), 1-8. | MR 232265 | Zbl 0155.44501

[5] J. Ne, Example of an irregular solution to a nonlinear elliptic system with analytic coefficients and conditions for regularity, Theory of Nonlinear Operators, Abhandlungen Akad. der Wissen. der DDR (1977), Proc. of a Summer School held in Berlin (1975). | MR 509483 | Zbl 0372.35031

[6] J. Nečas - O. John - J. Stará, Counterexample to the regularity of weak solutions of elliptic systems, Comment. Math. Univ. Carolinae 21 (1980), 145-154. | MR 566246 | Zbl 0442.35034

[7] J Nečas, Introduction to the theory of nonlinear elliptic equations, Teubner Texte zur Mathematik, Leipzig 1983. | MR 731261 | Zbl 0526.35003