Abstract
We prove global existence of strong solutions for two-dimensional parabolic systems of variational flow type subject to the one-sided condition.
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ARONSON, D.G.: Non-negative solutions of linear parabolic equations; Ann. Sc. Norm. Sup. Pisa,22(1968), 607–694
EELLS, J., J.H. SAMPSON: Harmonic mappings of Riemannian manifolds; Am. J. Math.86(1964), 109–160
FREHSE, J.: On Two-Dimensional Quasi-Linear Elliptic Systems, manusc. math.28(1979), 21–49
GIAQUINTA, M., M. STRUWE: An optimal regularity result for a class of quasilinear parabolic systems, manusc. math.36(1981), 223–239
GILBARG, D., N.S. TRUDINGER: Elliptic Partial Differential Equations of Second Order, Springer Grundlehren 224, Berlin, Heidelberg, New York, Tokyo, 2nd edition, 1983
HAMILTON, R.S.: Harmonic Maps of Manifolds with Boundary, Springer Lecture Notes 471, Berlin, Heidelberg, New York, 1975
HILDEBRANDT, S., H. KAUL, K.-O. WIDMAN: An Existence Theorem for Harmonic Mappings of Riemannian Manifolds, Acta Math.138 (1977), 1–16
JOST, J.: Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses; manusc. math.34(1981), 17–25
LADYSHENSKAYA, O.A., V.A. SOLONNIKOV, N.N. URAL'CEVA: Linear and Quasilinear Equations of Parabolic Type; Transl. Math. Monogr. 23, AMS, Providence, 1968
LIONS, J.L.: Quelques méthodes de résolution des problèmes aux limites non-linéaires, Dunod, Paris, 1969
MORREY, C.B. Jr.: Multiple Integrals in the Calculus of Variations, Springer, New York, 1966
STRUWE, M.: On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems; manusc. math.35(1981), 125–145
STRUWE, M.: Some regularity results for quasilinear parabolic systems, to appear in: Commentat. Math. Univ. Carol.
STRUWE, M.: On the evolution of harmonic mappings, to appear in: Comm. Math. Helv.
TOLKSDORF, P.: On some parabolic variational problems with quadratic growth, to appear in: Ann. Sc. Norm. Sup. Pisa
WAHL, W. VON: Verhalten der Lösungen parabolischer Gleichungen für t→∞ mit Lösbarkeit im Großen; Nachr. Akad. Wiss. Göttingen5(1981)
WIEGNER, M.: On two-dimensional elliptic systems with a one-sided condition, Math. Z.178(1981), 493–500
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Wieser, W. On parabolic systems with variational structure. Manuscripta Math 54, 53–82 (1985). https://doi.org/10.1007/BF01171700
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DOI: https://doi.org/10.1007/BF01171700