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<p>We study the set of (<i>p</i>,&#xa0;<i>q</i>)-eigenvalues of the <i>p</i>-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains.</p>

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ON THE (p, q)-EIGENVALUES OF THE NO-FLUX p-LAPLACIAN

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Alexander Menovschikov

摘要

We study the set of (p, q)-eigenvalues of the p-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains.