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- W157493467 abstract "Suppose $$mathcal{M}_0$$ is as in the introduction, and the gap condition there are adjacent $$,, v_0, w_0,, epsilon ,,mathcal{M}_0 ,,with ,,v_0 < w_0,,,,,,,,,,, ,,(*)_0$$ holds. Our goal is to show there are solutions of (PDE) heteroclinic in x1 from v0 to w0 and 1-periodic in the remaining variables. This requires introducing a class of admissible functions and an appropriate functional on this class whose minima will be the desired solutions of (PDE). As a first attempt, take the class of $$W_{loc}^{1,2}(mathbb{R} times {mathbb{T}^{n-1}})$$ functions that are asymptotic to v0 and w0 as x1 $$rightarrow pm infty $$ in some reasonableway and 2.1 $$ minimize int_{mathbb{R} times mathbb{T}^{n-1}} L(u)dx $$ over this class." @default.
- W157493467 created "2016-06-24" @default.
- W157493467 creator A5072200542 @default.
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- W157493467 date "2011-01-01" @default.
- W157493467 modified "2023-10-17" @default.
- W157493467 title "Function Spaces and the First Renormalized Functional" @default.
- W157493467 doi "https://doi.org/10.1007/978-0-8176-8117-3_2" @default.
- W157493467 hasPublicationYear "2011" @default.
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