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arXiv · 1509.06069

Sobolev-Trace inequalities of order four

Antonio Ache·Sun-Yung Alice Chang
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Abstract

We establish sharp Sobolev inequalities of order four on Euclidean d-balls for d greater than or equal to four. When d=4, our inequality generalizes the classical second order Lebedev-Milin inequality on Euclidean 2-balls. Our method relies on the use of scattering theory on hyperbolic d-balls. As an application, we charcaterize the extremals of the main term in the log-determinant formula corresponding to the conformal Laplacian coupled with the boundary Robin operator on Euclidean 4-balls.

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Antonio Ache, Sun-Yung Alice Chang. 2015-09-20. Sobolev-Trace inequalities of order four. https://doi.org/10.1215/00127094-2017-0014

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