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Symmetrization and second-order Sobolev inequalities. (English) Zbl 1223.46033

Summary: A Pólya-Szegő 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.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
26D10 Inequalities involving derivatives and differential and integral operators
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