Titlebook: Elliptic Systems of Phase Transition Type; Nicholas D. Alikakos,Giorgio Fusco,Panayotis Smyrn Book 2018 Springer Nature Switzerland AG 201

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https://doi.org/10.1007/978-3-663-02693-8This chapter together with Chap. . contain some general tools for obtaining estimates for systems.

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Introduction,In this chapter we give an overview of the book. We state and motivate the main theorems and refer the reader to the appropriate sections.

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The Cut-Off Lemma and a Maximum Principle,In this chapter we establish a maximum principle type result that provides pointwise control on minimal solutions. In contrast to the usual maximum principle, it does not hold for solutions in general, not even for local minimizers in the scalar case. We obtain it as a corollary of a replacement lemma modeled after Lemmas . and ..

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Nicholas D. Alikakos,Giorgio Fusco,Panayotis SmyrnCan be used as principal or supplementary reading for advanced graduate courses on nonlinear analysis or PDEs.Features a self-contained exposition of the existence of connections.Presents a new existe

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