On Liouville theorem and the regularity of weak solutions to some nonlinear elliptic systems of higher order. (English) Zbl 0773.35017

Balanda, L.; Viszus, E.

Commentat. Math. Univ. Carol. 32, No. 4, 615-625 (1991).

The aim of the paper is to extend the results of M. Giaquinta and J. Nečas [J. Reine Angew. Math. 316, 140-159 (1980; Zbl 0435.35036); Commentat. Math. Univ. Carol. 20, 111-122 (1979; Zbl 0396.35047)] from nonlinear systems of second order to nonlinear systems of any order. Namely, it is proved that Liouville’s property is a necessary and sufficient condition for the interior regularity of the solutions of the system.

Reviewer: L.Ambrosio (Roma)

MSC:

35J60	Nonlinear elliptic equations
35D10	Regularity of generalized solutions of PDE (MSC2000)
35G20	Nonlinear higher-order PDEs

Citations:

Zbl 0435.35036; Zbl 0396.35047