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/10.1007/978-3-642-71243-2xistence of stationary layered solutions in .. The Alama, Bronsard and Gui example is revisited in Chap. . under no symmetry hypotheses. Our results were originally obtained by a different method in Alikakos and Fusco (Annali della Scuola Normale Superiore di Pisa XV:809–836, 2016).

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,Symmetry and the Vector Allen–Cahn Equation: Crystalline and Other Complex Structures,f equivariant solutions. Our approach is variational and based on a mapping property of the parabolic vector Allen–Cahn equation and on a pointwise estimate for vector minimizers. The abstract results are then applied for particular choices of ., . and . : . → ., and solutions with complex symmetric structure are described.

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1421-1750 sition of the existence of connections.Presents a new existe.This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes – non-orientable objects with a stratified structure. The minimal solutions of the vector equation ex

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Book 2018table objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure not present in the scalar Allen-Cahn equation, which models coexistence of two phases and is related to minimal surfaces. The 1978 De Giorgi conjecture for the scalar problem was se

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Book 2018on of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions...• Preliminary material beginning with the stress-energy tensor, via which monoton