On the regularity for 2nd order nonlinear elliptic systems. (English) Zbl 0531.35033

Differential equations and their applications, Equadiff 5, Proc. 5th Czech. Conf., Bratislava 1981, Teubner-Texte Math. 47, 165-168 (1982).
[For the entire collection see Zbl 0507.00006.]
The paper is an instructive survey on questions related to the regularity of solutions to second order elliptic systems. Highlighted are the authors’ counterexamples in three and four dimensions [Comment. Math. Univ. Carol. 21, 145-154 (1980; Zbl 0442.35034)] and some relations between regularity and Liouville-type theorems [M. Giaquinta and the second author, ibid. 20, 111-121 (1979; Zbl 0396.35047); M. Giaquinta and the authors, Pac. J. Math. 99, 1-17 (1982; Zbl 0485.35020)].
Reviewer: B.Kawohl


35J60 Nonlinear elliptic equations
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs