Higher critical points in an elliptic free boundary problem
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Publication:1651369
DOI10.1007/S12220-017-9862-8zbMATH Open1391.35429arXiv1610.00799OpenAlexW2619451120MaRDI QIDQ1651369
Author name not available (Why is that?)
Publication date: 12 July 2018
Published in: (Search for Journal in Brave)
Abstract: We study higher critical points of the variational functional associated with a free boundary problem related to plasma confinement. Existence and regularity of minimizers in elliptic free boundary problems have already been studied extensively. But because the functionals are not smooth, standard variational methods cannot be used directly to prove the existence of higher critical points. Here we find a nontrivial critical point of mountain pass type and prove many of the same estimates known for minimizers, including Lipschitz continuity and nondegeneracy. We then show that the free boundary is smooth in dimension 2 and prove partial regularity in higher dimensions.
Full work available at URL: https://arxiv.org/abs/1610.00799
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