The ball locally minimizes F(E) = P_t(E)^{1/(n-t)} / P_s(E)^{1/(n-s)} (0 < s < t < 1) among nearly spherical sets, via quantitative stability of the rewritten functional in a Sobolev norm on the sphere.
Optimal embedding results for fractional Sobolev spaces
2 Pith papers cite this work. Polarity classification is still indexing.
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Authors prove Caccioppoli inequalities, local boundedness, Hölder continuity, weak Harnack inequalities, and expansion of positivity for weak solutions of mixed fractional superposition operators.
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Stability of the ball in isoperimetric inequalities between two fractional perimeters
The ball locally minimizes F(E) = P_t(E)^{1/(n-t)} / P_s(E)^{1/(n-s)} (0 < s < t < 1) among nearly spherical sets, via quantitative stability of the rewritten functional in a Sobolev norm on the sphere.
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Regularity of superposition operators of mixed fractional order
Authors prove Caccioppoli inequalities, local boundedness, Hölder continuity, weak Harnack inequalities, and expansion of positivity for weak solutions of mixed fractional superposition operators.