The continuity or stability method for nonlinear elliptic and parabolic equations and systems

[Ca] Campanato S.,On the nonlinear parabolic systems in divergence form. Hölder continuity and partial Hölder continuity of the solutions. Ann. Mat. Pura Appl. 137, 83–122, 1984.

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[G] Gerhardt C.,Stationary solutions to the Navier-Stokes equations in dimension four. Math. Z. 165, 193–197, 1970.

[GM1] Giaquinta M. and Modica L.,Non linear systems of the type of the stationary Navier-Stokes system. J. Reine Angew. Math. 330, 173–214, 1982.

[GM2] Giaquinta M. and Modica L.,Regularity results for some classes of higher order non linear elliptic systems. J. Reine Angew. Math. 311/312, 145–169, 1979.

[GS] Giaquinta M. and Struwe M.,An optimal regularity result for a class of quasilinear parabolic systems. Manuscripta math. 36, 223–239, 1981.

[GT] Gilbarg D. and Trudinger N.S.,Elliptic Partial Differential Equations of Second Order, 2nd Edition. Springer: Berlin, Heidelberg, New York, Tokyo,—1983.

[GrvW] Grunau H.C. and Wahl W. von,Regularity of Weak Solutions of Semilinear Parabolic Systems of Arbitrary Order. To appear. Preprint, 1991.

[H] Hamilton R.S.,Harmonic Maps of Manifolds with Boundary. Lecture Notes in Mathematics 471.— Springer: Berlin, Heidelberg, New York, 1975.

[HKW] Hildebrandt S., Kaul H. and Widman H.O.,An Existence Theorem for Harmonic Mappings of Riemannian Manifolds. Acta Math. 138, 1–16, 1977.

[J] Jäger W.,Ein Maximumprinzip fur ein System nichtlinearer Differentialgleichungen. Nachr. Ak. d. Wiss. Gottingen, II. Mathematisch-Physikalische Klasse, 1–29, 1978.

[JK] Jäger W. and Kaul H.,Uniqueness and Stability of Harmonic Maps and their Jacobi Fields. Manuscripta math. 28, 269–291, 1979.

[Jo] Jost J.,Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses. Manuscripta math. 34, 17–25, 1981.

[K] Kilimann N.,Ein Maximumprinzip fur nichtlineare parabolische Systeme, Math. Z. 171, 227–230, 1981.

[LU] Ladyžhenskaja O.A. and Ural'tseva N.N.,Linear-and Quasilinear Elliptic Equations, Academic Press: New York and London, 1968.

[LSU] Ladyžhenskaja O.A., Solonnikov V.A. and Ural'tseva N.N.,Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs 23. American Mathematical Society: Providence, R.I., 1968.

[LSvW] Lunardi A., Sinestrari E. and Wahl W. von,A semigroup approach to the time dependent parabolic initial boundary value problem. To appear in: Differential and Integral Equations. Preprint, 1989.

[L] Luckhaus S.,Existence and regularity of weak solutions to the Dirichlet problem for semilinear elliptic systems of higher order. J. Reine Angew. Math. 306, 192–207, 1979.

[S] Serrin J.,The initial value problem for the Navier-Stokes equations. University of Wisconsin Press: Madison, Wisconsin, Non-linear Problems, Proceedings of a Symposium, Madison 1962 (R. Langer ed.), 69–98, 1963.

[SvW] Sohr H., Wahl W. von,On the Singular Set and the Uniqueness of Weak Solutions of the Navier-Stokes Equations. Manuscripta math. 49, 27–59, 1984.

[T] Tomi F.,Über semilineare elliptische Differentialgleichungen zweiter Ordnung. Math. Z. 111, 350–366, 1969.

[W1] Wahl W. von,A-priori Schranken für semilineare und quasilineare parabolische Differentialgleichungen. Math. Z. 128, 93–108, 1972.

[W2] Wahl W. von,Über nichtlineare elliptische Gleichungen in der Ebene. Manuscripta math. 8, 59–67, 1973.

[W3] Wahl W. von,Existenzsätze für nichtlineare elliptische Systeme. Nachr.Ak.d. Wiss. Gottingen. II. Mathematisch-Physikalische Klasse, 131–177, 1981.

[W4] Wahl W. von,Klassische Lösbarkeit im Grossen fur nichtlineare parabolische Systeme und das Varhalten der Lösungen für t→∞. Nachr.Ak.d. Wiss. Gottingen, II. Mathematisch-Physikalische Klasse, 131–177, 1981.

[W5] Wahl W. von,Global Solutions to Evolution Equations of Parabolic Type. Lecture Notes in Mathematics 1223, Proceedings of the Conference on Differential Equations in Banach Spaces, Bologna 1985 (A. Favini and E. Obrecht editors), 254–266, 1986.

[W6] Wahl W. von,The Equations of Navier-Stokes and Abstract Parabolic Equations. Vieweg. Braunschweig, Wiesbaden, 1985.

[W7] Wahl W. von,Extension of a result of Ladyžhenskaja and Ural'tseva concerning second order parabolic equations to equations of arbitrary order. Ann. Pol. Math. 41, 63–72, 1983.

[Wi1] Wiegner M.,Ein optimaler Regularitätssatz fur schwache Lösungen gewisser elliptischer Systeme. —Math. Z. 147, 21–28, 1976.

[Wi2] Wiegner M.,On the Asymptotic Behaviour of Solutions of Non-linear Parabolic Equations, Math. Z. 188, 3–22, 1984.