Qualitative stability for a family of trace Sobolev inequalities
Abstract
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∈ (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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