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- W2912598839 abstract "In this chapter we begin the study of entire solutions (u:{mathbb R}^nrightarrow {mathbb R}^n) of the vector Allen–Cahn equation (6.1) that describe the coexistence of different phases in a neighborhood of a point. We work in a symmetry context where a finite reflection group G is acting both on the domain space ({mathbb R}_x^n) and on the target space ({mathbb R}_u^n), which are assumed to be of the same dimension. The scope of this chapter is to introduce the main ideas involved in the proof of Theorem 1.2 which invokes estimate ( 1.34) or alternatively the density estimate ( 1.28), but otherwise is self-contained. In Chap. 7 we present a systematic study of all symmetric entire solutions that can be obtained by a variational approach." @default.
- W2912598839 created "2019-02-21" @default.
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- W2912598839 date "2018-01-01" @default.
- W2912598839 modified "2023-09-23" @default.
- W2912598839 title "Symmetry and the Vector Allen–Cahn Equation: The Point Group in ℝn" @default.
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- W2912598839 doi "https://doi.org/10.1007/978-3-319-90572-3_6" @default.
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