Titlebook: Elliptic Partial Differential Equations of Second Order; David Gilbarg,Neil S. Trudinger Book 19771st edition Springer-Verlag Berlin Heide

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https://doi.org/10.1007/978-3-662-48870-6ear equations can be extended to higher dimensions by other methods. As will be seen, the special features of this theory are founded on strong apriori estimates that are valid for general . equations in two variables.

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Classical Solutions; the Schauder Approachm this fact Schauder [SC 4, 5] was able to construct a global theory, an extension of which is presented here. Basic to this approach are apriori estimates of solutions, extending those of potential theory to equations with Hölder continuous coefficients.

MOT

Topological Fixed Point Theorems and Their Applicationst formulate a general criterion for solvability and illustrate its application in a situation where the required apriori estimates are readily derived from our previous results. The derivation of these apriori estimates under more general hypotheses will be the major concern of the ensuing chapters.

Terminal

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https://doi.org/10.1007/978-3-662-08569-1ber field. The theory of this chapter, however, carries over almost unchanged if the real numbers are replaced by the complex numbers. Let ? be a linear space over ℝ. A . on . is a mapping . : . → ℝ (henceforth we write .(.) = ‖ . ‖ = ‖ . ‖., . ∊ .) satisfying

Calculus

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Banach and Hilbert Spacesber field. The theory of this chapter, however, carries over almost unchanged if the real numbers are replaced by the complex numbers. Let ? be a linear space over ℝ. A . on . is a mapping . : . → ℝ (henceforth we write .(.) = ‖ . ‖ = ‖ . ‖., . ∊ .) satisfying

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Equations of Mean Curvature Types Laplace’s equation. In particular we shall derive an extension of the classical result of Bernstein that a ..(ℝ.) solution of the minimal surface equation in ℝ. must be a linear function (Theorem 15.12).