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.

Best constants and minimizers for embeddings of second order Sobolev spaces / Berchio, Elvise; F., Gazzola. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 328:(2006), pp. 718-735. [10.1016/j.jmaa.2005.07.052]

### Best constants and minimizers for embeddings of second order Sobolev spaces

#### 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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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2522495`