The aim of this paper is to show that Liouville type property is a sufficient and necessary condition for the regularity of weak solutions of nonlinear elliptic systems of the higher order.
@article{118441, author = {Lubom\'\i r Balanda and Eugen Viszus}, title = {On Liouville theorem and the regularity of weak solutions to some nonlinear elliptic systems of higher order}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {615-625}, zbl = {0773.35017}, mrnumber = {1159808}, language = {en}, url = {http://dml.mathdoc.fr/item/118441} }
Balanda, Lubomír; Viszus, Eugen. On Liouville theorem and the regularity of weak solutions to some nonlinear elliptic systems of higher order. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 615-625. http://gdmltest.u-ga.fr/item/118441/
On Liouville theorem and Hölder continuity of weak solutions to some quasilinear elliptic systems of higher order, to appear. | MR 1197287 | Zbl 0817.35015
On the regularity of weak solutions to non-linear elliptic systems of partial differential equations, J. Reine Angew. Math. 316 (1980), 140-159. (1980) | MR 0581329
On the regularity of weak solutions to nonlinear elliptic systems via Liouville's type property, Comment. Math. Univ. Carolinae 20 (1979), 111-122. (1979) | MR 0526152 | Zbl 0396.35047
Function Spaces, Academia, Prague, 1977. | MR 0482102
Introduction to the theory of non-linear elliptic equations, Teubner-Texte zur Mathematik, Leipzig, 1983. | MR 0731261
Les méthodes directes en Théorie des équations elliptiques, Academia, Prague, 1967. | MR 0227584