This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The applications, however, require a fair knowledge of classical analysis and PDEs which is needed to make judicious choices of function spaces where the self-dual variational principles need to be applied, and these choices necessarily require prior knowledge of the expected regularity of the (weak) solutions. While this text contains many new results, it is the author's hope that this material will soon become standard for all graduate students.
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