ABSTRACT Let , , and be an open bounded domain in with smooth boundary. We consider the minimum problem over a certain class , where and are constants, and . The corresponding Euler–Lagrange equation is related to the Ginzburg–Landau equation and involves a subcritical exponent when . For and , we prove the existence, non‐negativity, and uniform boundedness of minimizers of . Then, we show that any minimizer is locally ‐continuous with some and admits the optimal growth near the free boundary. Finally, under the additional assumption that , we establish non‐degeneracy for minimizers near the free boundary and show that there exists at least one minimizer for which the corresponding free boundary has finite ()‐dimensional Hausdorff measure.
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Yi Hu
Jun Zheng
Leandro S. Tavares
Mathematische Nachrichten
Universidade Estadual de Campinas (UNICAMP)
Southwest Jiaotong University
Universidade Federal do ABC
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Hu et al. (Tue,) studied this question.
www.synapsesocial.com/papers/69c6202f15a0a509bde189fe — DOI: https://doi.org/10.1002/mana.70134