Abstract
A Pólya–Szegö principle for second-order derivatives is established. As a consequence, a new unified approach to second-order Sobolev-type inequalities, via 1-dimensional inequalities, is derived. Applications to some optimal Sobolev embeddings are exhibited.
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Mathematics Subject Classification (2000)
46E35, 46E30
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Cianchi, A. Symmetrization and second-order Sobolev inequalities. Ann. Mat. Pura Appl. IV. Ser. 183, 45–77 (2004). https://doi.org/10.1007/s10231-003-0080-6
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DOI: https://doi.org/10.1007/s10231-003-0080-6