Displaying similar documents to “Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed L p -norm.”

Mixed norms and Sobolev type inequalities

V. I. Kolyada (2006)

Banach Center Publications

Similarity:

We study mixed norm spaces that arise in connection with embeddings of Sobolev and Besov spaces. We prove Sobolev type inequalities in terms of these mixed norms. Applying these results, we obtain optimal constants in embedding theorems for anisotropic Besov spaces. This gives an extension of the estimate proved by Bourgain, Brezis and Mironescu for isotropic Besov spaces.

Variable Sobolev capacity and the assumptions on the exponent

Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)

Banach Center Publications

Similarity:

In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.

On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations

W. M. Zajączkowski

Similarity:

The existence and uniqueness of solutions of an initial-boundary value problem for the second order linear parabolic system which appears in free boundary problems for compressible Navier-Stokes equations are proved. Moreover, an estimate in anisotropic Sobolev-Slobodetskii spaces with noninteger derivatives is found. The existence and regularity of solutions are shown by means of a regularizer in the same way as in the case of general parabolic systems. However, the problem must be...

Dimension-invariant Sobolev imbeddings

Miroslav Krbec, Hans-Jürgen Schmeisser (2011)

Banach Center Publications

Similarity:

We survey recent dimension-invariant imbedding theorems for Sobolev spaces.