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

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)


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