On the loss of compactness in the vectorial heteroclinic connection problemKatzourakis, N. (2016) On the loss of compactness in the vectorial heteroclinic connection problem. Proceedings of the Royal Society of Edinburgh A, 146 (3). pp. 595-608. ISSN 1473-7124 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1017/S0308210515000700 Abstract/SummaryWe give an alternative proof of the theorem of Alikakos and Fusco concerning existence of heteroclinic solutions U : ℝ → ℝ N to the system Here a± are local minima of a potential W ∈ C2(ℝ N ) with W(a±) = 0. This system arises in the theory of phase transitions. Our method is variational but differs from the original artificial constraint method of Alikakos and Fusco and establishes existence by analysing the loss of compactness in minimizing sequences of the action in the appropriate functional space. Our assumptions are slightly different from those considered previously and also imply a priori estimates for the solution.
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