Calculus of Variations and Geometric Measure Theory
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E. Berchio - F. Gazzola

Best constants and minimizers for embeddings of second order Sobolev spaces

created by gazzola on 30 May 2005
modified on 16 Sep 2005

[BibTeX]

Accepted Paper

Inserted: 30 may 2005
Last Updated: 16 sep 2005

Year: 2005

Abstract:

By considering the kernels of the first two traces, four different second order Sobolev spaces may be constructed. For these spaces, embeddings into Lebesgue spaces, the best embedding constant and the possible existence of minimizers are studied. The Euler equation corresponding to some of these minimization problems is a semilinear biharmonic equation with boundary conditions involving third order derivatives: it is shown that the complementing condition is satisfied.


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