Qualitative stability for a family of trace Sobolev inequalities
classification
🧮 math.AP
keywords
familyinequalitiesstabilityqualitativesobolevtraceanalysisanswers
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The goal of this short note is to prove qualitative stability for a family of trace Sobolev inequalities first proven by Carlen \& Loss for $p=2$ and by Maggi and the author for $p\in (1,n)$. This answers an open problem raised in a recent paper of Fan, Li \& Zhang, and in conjunction with their local analysis, yields sharp quantitative stability for this family of inequalities when $p=2$.
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