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<p>In this paper, we investigate the extremal functions for anisotropic Trudinger-Moser inequalities. Our method uses convex symmetrization, the continuity of the supremum function, together with the relation between the supremums of the subcritical and the critical anisotropic Trudinger-Moser inequality, we give some results of existence and symmetry about the extremal functions for several different types of anisotropic Trudinger-Moser inequalities.</p>

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Existence of Extremal Functions and Wulff Symmetry for Anisotropic Trudinger-Moser Inequalities

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Kaiwen Guo,
  • Yanjun Liu

摘要

In this paper, we investigate the extremal functions for anisotropic Trudinger-Moser inequalities. Our method uses convex symmetrization, the continuity of the supremum function, together with the relation between the supremums of the subcritical and the critical anisotropic Trudinger-Moser inequality, we give some results of existence and symmetry about the extremal functions for several different types of anisotropic Trudinger-Moser inequalities.