Sharp Gradient Stability for the Sobolev Trace Inequality

2026/07/20 by Xi-Nan Ma, Yitian Zhang, Yang Zhou · 1 citation
#math.AP

paper · pdf

Abstract

Let \(n≥3\) and \(1<p<n\). We prove a quantitative stability estimate for the critical Sobolev trace inequality on the upper half-space. More precisely, the Sobolev trace deficit controls the \(max\2,p\\)-th power of the gradient distance to the manifold of trace bubbles. A central part of the proof is the spectral nondegeneracy of the trace bubbles: the first two eigenspaces of the linearized weighted Steklov problem are exactly the amplitude, dilation, and tangential translation modes.

Cited by

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

Related

• Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality
• Gradient stability for the Sobolev inequality: the case p≥ 2
• On the stability of fractional Sobolev trace inequality and corresponding profile decomposition
• Sharp gradient stability for the Sobolev inequality
• Sharp stability for critical points of the Sobolev inequality in the absence of bubbling