Abstract
In this chapter we shall need the fundamental concept of Hölder continuity, which we now recall from Sect. 11.1:
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- 1.
“sup ” here is the essential supremum, as explained in the appendix.
References
Ahlfors, L.: Complex Analysis. McGraw Hill, New York (1966)
Bers, L., Schechter, M.: Elliptic equations. In: Bers, L., John, F., Schechter, M. (eds.) Partial Differential Equations, pp. 131–299. Interscience, New York (1964)
Braess, D.: Finite Elemente. Springer, Berlin (1997)
Chavel, I.: Eigenvalues in Riemannian Geometry. Academic, Orlando (1984)
Courant, R., Hilbert, D.: Methoden der Mathematischen Physik, vol. I and II, reprinted 1968, Springer. Methods of mathematical physics. Wiley-Interscience, vol. I, 1953, Vol. II, 1962, New York (the German and English versions do not coincide, but both are highly recommended)
Crandall, M., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277, 1–42 (1983)
Evans, L.C.: Partial differential equations. Graduate Studies in Mathematics, vol. 19, AMS (2010)
Frehse, J.: A discontinuous solution to a mildly nonlinear elliptic system. Math. Zeitschr. 134, 229–230 (1973)
Friedman, A.: Partial Differential Equations of Parabolic Type. Prentice Hall, Englewood Cliffs (1964)
Giaquinta, M.: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Princeton University Press, Princeton (1983)
Giaquinta, M.: Introduction to Regularity Theory for Nonlinear Elliptic Systems. Birkhäuser, Basel (1993)
Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second Order. Springer, Berlin (1983)
Hildebrandt, S., Kaul, H., Widman, K.O.: An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math. 138, 1–16 (1977)
John, F.: Partial Differential Equations. Springer, New York (1982)
Jost, J.: Generalized Dirichlet forms and harmonic maps. Calc. Var. Partial Differ. Equ. 5, 1–19 (1997)
Jost, J.: Nonpositive Curvature: Geometric and Analytic Aspects. Birkhäuser, Basel (1997)
Jost, J.: Dynamical Systems. Springer, Berlin (2005)
Jost, J.: Postmodern Analysis. Springer, Berlin (1998)
Jost, J.: Postmodern Analysis. Springer, Berlin (2005)
Jost, J.: Riemannian Geometry and Geometric Analysis. Springer, Berlin (2011)
Jost, J., Li-Jost, X.: Calculus of Variations. Cambridge University Press, Cambridge (1998)
Kolmogoroff, A., Petrovsky, I., Piscounoff, N.: Étude de l’ équation de la diffusion avec croissance de la quantité de la matière et son application à un problème biologique. Moscow Univ. Bull. Math.1, 1–25 (1937)
Ladyzhenskya, O.A., Solonnikov, V.A., Ural’tseva, N.N.: Linear and quasilinear equations of parabolic type. Amer. Math. Soc. (1968)
Ladyzhenskya, O.A., Ural’tseva, N.N.: Linear and Quasilinear Elliptic Equations. Nauka, Moskow, 1964 (in Russian); English translation: Academic Press, New York, 1968, 2nd Russian edition 1973
Lasota, A., Mackey, M.: Chaos, Fractals, and Noise. Springer, New York (1994)
Lin, F.H.: Analysis on singular spaces. In: Li, T.T. (ed.) Geometry, Analysis and Mathematical Physics, in Honor of Prof. Chaohao Gu, 114–126, World Scientific (1997)
Moser, J.: On Harnack’s theorem for elliptic differential equations. Comm. Pure Appl. Math. 14, 577–591 (1961)
Murray, J.: Mathematical Biology. Springer, Berlin (1989)
Smoller, J.: Shock Waves and Reaction-Diffusion Equations. Springer, New York (1983)
Strang, G., Fix, G.: An Analysis of the Finite Element Method. Prentice Hall, Englewood Cliffs (1973)
Taylor, M.: Partial Differential Equations, vol. I–III. Springer, Berlin (1996)
Yosida, K.: Functional Analysis. Springer, Berlin (1978)
Zeidler, E.: Nonlinear Functional Analysis and Its Applications, vol. I–IV. Springer, New York (1984)
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Jost, J. (2013). The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV). In: Partial Differential Equations. Graduate Texts in Mathematics, vol 214. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4809-9_13
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