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Liouville theorems for nonlinear elliptic equations and systems. (English) Zbl 0426.35034

MSC:
35J60 Nonlinear elliptic equations
35B45 A priori estimates in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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[1] FREHSE, J., Essential selfadjointness of singular elliptic operators. Preprint no. 116 of the SFB 72, Universit?t Bonn (1977) · Zbl 0448.47029
[2] HILDEBRANDT, S. and WIDMAN, K.-O., Some regularity results for quasilinear elliptic systems of second order. Math. z., 142, 67-86 (1975) · Zbl 0317.35040 · doi:10.1007/BF01214849
[3] HILDEBRANDT, S. and WIDMAN, K.-O., On the H?lder continuity of weak solutions of quasilinear elliptic systems of second order. Annali Scuola Norm. Sup. Pisa, IV, 1, 145-178 (1977) · Zbl 0353.35013
[4] HILDEBRANDT, S. and WIDMAN, K.-O., S?tze vom Liouvilleschen Typ f?r quasilineare elliptische Gleichungen und Systeme. Nachrichten der Akad. Wiss. G?ttingen, to appear · Zbl 0426.35037
[5] IVANOV, A.V., Local estimates for the first derivatives of solutions of quasilinear second order elliptic equations and their application to Liouville type theorems. Seminar Steklov Inst. Leningrad, 30, 40-50 (1972). Translation in: J. Sov. Math., 4, 335-344 (1975)
[6] MEIER, M., Regul?re und singul?re L?sungen quasilinearer elliptischer Gleichungen und Systeme. Dissertation, Bonn 1978
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[8] PELETIER, L.A. and SERRIN, J., Gradient bounds and Liouville theorems for quasilinear elliptic equations. Annali Scuola Norm. Sup. Pisa, IV, 5, 65-104 (1978) · Zbl 0383.35025
[9] SERRIN, J., Local behavior of solutions of quasilinear equations. Acta Math., 111, 247-302 (1964) · Zbl 0128.09101 · doi:10.1007/BF02391014
[10] SERRIN, J., Liouville theorems and gradient bounds for quasilinear elliptic systems. Archive Rat. Mech. Anal., 66, 295-310 (1977) · Zbl 0368.35034 · doi:10.1007/BF00250675
[11] TRUDINGER, N.S., On Harnack type inequalities and their application to quasilinear elliptic equations. Comm. Pure Appl. Math., 20, 721-747 (1967) · Zbl 0153.42703 · doi:10.1002/cpa.3160200406
[12] WIEGNER, M., ?ber die Regularit?t schwacher L?sungen gewisser elliptischer Systeme. Manuscripta Math., vol. 15, 365-384 (1975) · Zbl 0312.35035 · doi:10.1007/BF01486606
[13] WIEGNER, M., Ein optimaler Regularit?tssatz f?r schwache L?sungen gewisser elliptischer Systeme. Math. z., 147, 21-28 (1976) · Zbl 0316.35039 · doi:10.1007/BF01214271
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