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Ball Rigidity of Local Minimizing Domains for the Best Fractional Sobolev Constant: The Subquadratic Case
After Corollary 1.3 in Calculus of Variations and Partial Differential Equations 60 (2021), Paper 231, Djitte, Fall, and Weth asked whether, when $1<p<2$, a volume-constrained local minimizing domain for the best fractional Sobolev constant must still be a ball. This paper solves that problem. Let $
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