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References
Baldes, A., Degenerate elliptic operators, diagonal systems and variational integrals; manuscripta math. 55, 467–486 (1986).
Bers, L., Isolated singularities of minimal surfaces; Ann. of Math. (2) 53, 364–386 (1951).
Buser, P., and H. Karcher, Gromov’s almost flat manifolds; Astérisque 81 (1981).
Caffarelli, L.A., Regularity theorems for weak solutions of some nonlinear systems; Comm. Pure Appl. Math. 35, 833–838 (1982).
Donelly, H., Bounded harmonic functions and positive Ricci curvature; Math. Z. 191, 559–565 (1986).
Fabes, E.B., C.E. Kenig, and R.P. Serapioni, The local regularity of solutions of degenerate elliptic equations; Comm. P.D.E. 7 (1), 77–116 (1982).
Finn, R., Isolated singularities of solutions to non-linear partial differential equations; Trans. Amer. Math. Soc. 75, 385–404 (1953).
Finn, R., and D. Gilbarg, Three-dimensional subsonic flows, and asymptotic estimates for elliptic partial differential equations; Acta Math. 98 265–296 (1957).
Frehse, J., A discontinuous solution of a mildly nonlinear elliptic system; Math. Z. 134, 229–230 (1973).
Giaquinta, M., and E. Giusti, On the regularity of the minima of variational integrals; Acta Math. 148, 31–45 (1982).
Giaquinta, M., and S. Hildebrandt, A priori estimates for harmonic mappings; J. reine angew. Math. 336, 124–164 (1982).
Gilbarg, D., and J. Serrin, On isolated singularities of solutions of second order elliptic differential equations; J. Analyse Math. 4, 309–340 (1955–1956).
Gilbarg, D., and N. S. Trudinger, Elliptic partial differential equations of second order; Springer, Berlin/Heidelberg/New York (1977).
Hildebrandt, S., and K.-O. Widman, Some regularity results for quasilinear elliptic systems of second order; Math. Z. 142, 67–86 (1975).
Hildebrandt, S., and K.-O. Widman, On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order; Ann. Scuola Norm. Sup. Pisa (IV), 4, 145–178 (1977).
Hildebrandt, S., and K.-O. Widman, Sätze vom Liouvilleschen Typ fÜr quasilineare elliptische Gleichungen und Systeme; Nachrichten der Akad. Wiss. Göttingen, II. Math.-Phys. Klasse, Nr. 4, 41–59 (1979).
Hildebrandt, S., H. Kaul, and K.-O. Widman, An existence theory for harmonic mappings of Riemannian manifolds; Acta Math. 138, 1–16 (1977).
Hildebrandt, S., J. Jost, and K.-O. Widman, Harmonic mappings and minimal submanifolds; Inventiones math. 62, 269–298 (1980).
Hildebrandt, S., Liouville theorems for harmonic mappings and an approach to Bernstein theorems; in "Seminar on Diff. Geometry", ed. S.-T. Yau, Annals of Math. Studies 102, 107–131, Princeton Univ. Press, 1982.
Hildebrandt, S., Nonlinear elliptic systems and harmonic mappings; Proc. of the 1980 Beijing Symposium of Diff. Geom. and Diff. Equ., Vol. 1, pp. 481–615, Science Press, Beijing, China 1982.
Hildebrandt, S., Quasilinear elliptic systems in diagonal form; in "Systems of nonlinear partial differential equations", ed. J.M. Ball, Reidel, Dordrecht/Boston/Lancester (1983).
Hildebrandt, S., Harmonic mappings of Riemannian manifolds; in "Harmonic mappings and minimal immersions", ed. E. Giusti, Springer Lecture Notes in Math. 1161, 1–117 (1985).
Ivert, P.-A., On quasilinear elliptic systems of diagonal form; Math. Z. 170, 283–286 (1980).
Jäger, W., Ein Maximumsprinzip für ein System nichtlinearer Differentialgleichungen; Nachrichten der Akad. Wiss. Göttingen 11, 157–164 (1976).
Karp, L., Subharmonic functions on real and complex manifolds; Math. Z. 179, 535–554 (1982).
Lawson, H.B., and R. Osserman, Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system; Acta Math. 139, 1–17 (1977).
Lin, F.H., and W.M. Ni, On the least growth of harmonic functions and the boundary behavior of Riemann mappings; Comm. P.D.E. 10(7), 767–786 (1985).
Meier, M., Liouville theorems for nonlinear elliptic equations and systems; manuscripta math. 29, 207–228 (1979).
Meier, M., Liouville theorems for nondiagonal elliptic systems in arbitrary dimensions; Math. Z. 176, 123–133 (1981).
Meier, M., Removable singularities for weak solutions of quasilinear elliptic systems; J. reine angew. Math. 344,87–101 (1983).
Meier, M., Removable singularities of harmonic maps and an application to minimal submanifolds; Indiana Univ. Math. J. 35, 705–726 (1986).
Meier, M., On quasilinear elliptic systems with quadratic growth; Preprint 1984.
Moser, J., On Harnack’s theorem for elliptic differential equations; Comm. Pure Appl. Math. 14, 577–591 (1961).
Osserman, R., A hyperbolic surface in 3-space; Proc. Amer. Math. Soc. 7, 54–58 (1956).
Osserman, R., Minimal varieties; Bull. Amer. Math. Soc. 75, 1092–1120 (1969).
Ruh, E.A., and J. Vilms, The tension field of the Gauss map; Trans. Amer. Math. Soc. 149, 569–573 (1970).
Serrin, J., Local behavior of solutions of quasilinear equations; Acta Math. 111, 247–302 (1964).
Serrin, J., Singularities of solutions of nonlinear equations; Proc. Symp. Appl. Math. Amer. Math. Soc. 17, 68–88 (1965).
Serrin, J., and H.F. Weinberger, Isolated singularities of solutions of linear elliptic equations; Amer. J. Math. 88, 258–272 (1966).
Simon, L., Asymptotic behaviour of minimal graphs over exterior domains; Ann. Inst. Henri Poincaré, Analyse non linéaire 4, 231–242 (1987).
Stredulinski, E.W., Weighted inequalities and degenerate partial differential equations; Springer Lecture Notes in Math. 1074 (1984).
Trudinger, N.S., On Harnack type inequalities and their application to quasilinear elliptic equations; Comm. Pure Appl. Math. 20, 721–747 (1967).
Wiegner, M., Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer Systeme; Math. Z. 147, 21–28 (1976).
Wiegner, M., A-priori Schranken für Lösungen gewisser elliptischer Systeme; manuscripta math. 18, 279–297 (1976).
Wiegner, M., Das Existenz-und Regularitätsproblem bei Systemen nichtlinearer elliptischer Differentialgleichungen; Habilitationsschrift, Bochum (1977).
Wiegner, M., On two-dimensional elliptic systems with a one-sided condition; Math. Z. 178, 493–500 (1981).
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Meier, M. (1988). Asymptotic behavior of solutions of some quasilinear elliptic systems in exterior domains. In: Hildebrandt, S., Leis, R. (eds) Partial Differential Equations and Calculus of Variations. Lecture Notes in Mathematics, vol 1357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082872
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