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Classification Theorem For Positive Critical Points Of Sobolev Trace Inequality

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arxiv 2402.17602 v4 pith:PEZ3QQOT submitted 2024-02-27 math.AP math.FA

Yang Zhou This is my paper · ORCID
classification math.APmath.FA
keywords equationinequalitysobolevtracepositiveclassificationeuler-lagrangemethod
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abstract

We consider the Euler-Lagrange equation of Sobolev trace inequality and prove several classification results. Exploiting the moving sphere method, it has been shown, when $p=2$, positive solutions of Euler-Lagrange equation of Sobolev trace inequality are classified. Since the moving sphere method strongly relies on the symmetries of the equation, in this paper we use asymptotic estimates and two important integral identities to classify positive solutions of Euler-Langrange equation of Sobolev trace inequality under finite energy when $1<p<n$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sharp Gradient Stability for the Sobolev Trace Inequality

    math.AP 2026-07 conditional novelty 7.0 of 10

    The Sobolev trace deficit controls the max{2,p}-th power of the gradient distance to the trace-bubble manifold for all 1<p<n.

  2. Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality

    math.AP 2026-07 conditional novelty 5.0 of 10

    Near one trace bubble, the Euler-Lagrange residual controls the L^p-gradient distance with sharp power max{1,p-1}, and a Struwe-type compactness decomposition holds.

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