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On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems. (English) Zbl 0519.35007


MSC:

35B65 Smoothness and regularity of solutions to PDEs
35K55 Nonlinear parabolic equations

Citations:

Zbl 0164.123
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References:

[1] ARONSON, D.G.: Non-negative solutions of linear parabolic equations. Ann. Sc. Norm. Sup. Pisa22, 607-694 (1968) · Zbl 0182.13802
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[3] DA PRATO, G.: Spazi(p, ?)(?, ?) e loro proprietá. Ann. Mat. Pura Appl.69, 383-392 (1965) · Zbl 0145.16207
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[6] FREHSE, J.: Capacity methods in the theory of partial differential equations, to appear · Zbl 0486.35002
[7] HILDEBRANDT, S. - WIDMAN, K.-O.: Some regularity results for quasilinear elliptic systems of second order. Math. Z.142, 67-86 (1975) · Zbl 0317.35040
[8] HILDEBRANDT, S. - WIDMAN, K.-O.: On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order. Ann. Sc. Norm. Sup. Pisa Ser. 4,4, 145-178 (1977) · Zbl 0353.35013
[9] KUFNER, A. - JOHN, O. - FUCIK, A.: Function spaces. Academia, Prague (1977)
[10] LADYSHENSKAYA, O.A. - SOLONNIKOV, V.A. - URAL’CEVA, N.N.: Linear and quasilinear equations of parabolic type. Translations Math. Monogr.23, AMS, Providence, R.I. (1968)
[11] LADYSHENSKAYA, O.A. - URAL’CEVA, N.N.: Linear and quasilinear elliptic equations. Academic Press, New York (1968)
[12] MOSER, J.: A Harnack inequality for parabolic differential equations. Comm. Pure Appl. Math.17, 101-134 (1964) · Zbl 0149.06902
[13] SPERNER, E., jr.: Ein Regularitätssatz für Systeme nichtlinearer elliptischer Differentialgleichungen. Math. Z.146, 57-68 (1976) · Zbl 0319.35037
[14] WIDMAN, K.-O.: Hölder continuity of solutions of elliptic systems, manusc. math.5, 299-308 (1971) · Zbl 0223.35044
[15] WIEGNER, M.: Über die Regularität schwacher Lösungen gewisser elliptischer Systeme. manusc. math.15, 365-384 (1975) · Zbl 0312.35035
[16] WIEGNER, M.: Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer Systeme. Math. Z.147, 21-28 (1976) · Zbl 0316.35039
[17] WIEGNER, M.: A-priori Schwanken für Lösungen gewisser elliptischer Systeme. manusc. math.18, 279-297 (1976) · Zbl 0323.35032
[18] WIEGNER, M.: Das Existenz- und Regularitätsproblem bei Systemen nichtlinearer elliptischer Differentialgleichungen, Habilitationsschrift, Bochum (1977)
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