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

2026/07/23 by Bao Yu, Yang Zhou
#math.AP

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Abstract

Let n≥3 and 1<p<n. We first prove the local trace analogue of the sharp one-bubble critical-point stability theorem of Liu and Zhang~\citeLiuZhang2025: near a positive trace-bubble, the Euler--Lagrange residual controls the gradient distance to the normalized trace-bubble manifold with the sharp power max\1,p-1\. Then, we establish a Struwe-type compactness theorem for the critical trace functional, which gives the trace counterpart of the Mercuri--Willem decomposition~\citeMercuriWillem2010. Combining Struwe-type compactness with the local stability estimate yields a sharp quantitative one-bubble critical-point stability theorem.

Citations

• Sharp Gradient Stability for the Sobolev Trace Inequality

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