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Balanda, Lubomír ; Viszus, Eugen
On Liouville theorem and Hölder continuity of weak solutions to some quasilinear elliptic systems of higher order. (English). Mathematica Bohemica, vol. 117 (1992), issue 4, pp. 373-392
MSC: 35B65, 35D10, 35J45, 35J60 | MR 1197287 | Zbl 0817.35015 | DOI: 10.21136/MB.1992.126063
Keywords:
Liouville property; regularity; regularity of weak solutions; quasilinear elliptic systems
Summary:
The aim of this paper is to show that the Liouville-type property is a sufficient and necessary condition for the regularity of weak solutions of quasilinear elliptic systems of higher orders.
References:
[1] Giaquinta M., Nečas J.: On the regularity of weak solutions to non-linear elliptic systems of partial differential equations. J. Reine Angew. Math. 316 (19S0), 140-159. MR 0581329
[2] Giaquinta M., Nečas J.: On the regularity of weak solutions to non-linear elliptic systems via Liouville's type property. Comm. Math. Univ. Carol. 50 (1979), 111-122. MR 0526152
[3] Giusti E.: Regolaritá parziale delle soluzioni di sistemi ellittici quasi lineari di ordine arbitrario. Ann. Scuola Norm. Sup. Pisa 23 (1969), 115-141. MR 0247258
[4] Kawohl B.: On Liouville theorem, continuity and Hölder continuity of weak solution to some quasilinear elliptic systems. Comm. Math. Univ. Carol. 21 (1980), 679-697. MR 0597758
[5] Kufner A., Fučík S., John O.: Function Spaces. Academia, Prague, 1977. MR 0482102
[6] Meier M.: Liouville theorems for non-linear elliptic equations and systems. Manuscripta Math. 29 (1979), 207-228. DOI 10.1007/BF01303628 | MR 0545042
[7] Nečas J.: Introduction to the theory of nonlinear elliptic equations. Teubner-Text zur Mathematik, Leipzig, 1983. MR 0731261
[8] Nečas J.: Les méthodes directes en théorie des equations elliptiques. Academia, Prague, 1967. MR 0227584
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