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Article

Balanda, L. ; Viszus, E.
On Liouville theorem and the regularity of weak solutions to some nonlinear elliptic systems of higher order. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 32 (1991), issue 4, pp. 615-625
MSC: 35D10, 35G20, 35J45, 35J60 | MR 1159808 | Zbl 0773.35017
Keywords:
regularity of weak solutions; nonlinear elliptic systems
Summary:
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.
References:
[1] Balanda L., Viszus E.: On Liouville theorem and Hölder continuity of weak solutions to some quasilinear elliptic systems of higher order. to appear. MR 1197287 | Zbl 0817.35015
[2] Giaquinta M., Nečas J.: On the regularity of weak solutions to non-linear elliptic systems of partial differential equations. J. Reine Angew. Math. 316 (1980), 140-159. MR 0581329
[3] Giaquinta M., Nečas J.: On the regularity of weak solutions to nonlinear elliptic systems via Liouville's type property. Comment. Math. Univ. Carolinae 20 (1979), 111-122. MR 0526152 | Zbl 0396.35047
[4] Fučík S., John O., Kufner A.: Function Spaces. Academia, Prague, 1977. MR 0482102
[5] Nečas J.: Introduction to the theory of non-linear elliptic equations. Teubner-Texte zur Mathematik, Leipzig, 1983. MR 0731261
[6] Nečas J.: Les méthodes directes en Théorie des équations elliptiques. Academia, Prague, 1967. MR 0227584
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