Titlebook: Nonlinear Elliptic Partial Differential Equations; An Introduction Hervé Le Dret Textbook 2018 Springer International Publishing AG, part o

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Fixed Point Theorems and Applications,rential equations problems, may be recast as problems of finding a fixed point of a certain mapping in a certain space. We will see several examples of this a little later on. It is therefore interesting to have fixed point theorems at our disposal that are as general as possible.

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Monotone Operators and Variational Inequalities,re generally of quasi-monotone operator, makes it possible to go further than the calculus of variations in the convex case. They are associated with variational inequalities, which appear in many situations, such as obstacle problems for example.

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A Brief Review of Real and Functional Analysis,This chapter is meant to provide a very quick review of the real and functional analysis results that will be most frequently used afterwards. Missing proofs can be found in most classical works dealing with these questions.

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Superposition Operators,In the previous chapter, when studying the model problem ??Δ.?=?.(.), we have already met operators of the form .?.(.) where . is a mapping from . to ., and . belongs to some function space defined over an open subset of .. This type of operator is called a . or .. Let us now study these operators in more detail in various functional contexts.

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