The Sobolev spaces have played an essential role in the research of partial differential equations ever since the mid thirties. In order to handle boundary value problems, and, in particular, traces, the more general scales of space have been introduced, namely Slobodeckii spaces and Besov spaces. It proved that Besov spaces are a suitable replacement for Sobolev spaces in many situations and t...

This paper is concerned with the Besov regularity of the solutions to interface problems in a segment S of the unit disk in R 2 : We investigate the smoothness of the solutions as measured in the speciic scale B s (L (S)); 1== = s=2+1=p; of Besov spaces which determines the order of approximation that can be achieved by adap-tive and nonlinear numerical schemes. The proofs are based on represen...

In this paper, we prove that the generator of any bounded analytic semigroup in (θ, 1)-type real interpolation its domain and underlying Banach space has maximal L1-regularity, using a duality argument combined with result continuous regularity. As an application, consider L1-regularity Dirichlet-Laplacian Stokes operator inhomogeneous B ,1 -type Besov spaces on domains ℝn, n ≥ 2.

Keywords: Boundary value problems Differential-operator equations Banach-valued Besov spaces Operator-valued multipliers Interpolation of Banach spaces a b s t r a c t The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, t...

We characterize local embeddings of Besov spaces B p,r involving only a slowly varying smoothness b into classical Lorentz spaces. These results are applied to establish sharp local embeddings of Besov spaces in question into Lorentz-Karamata spaces. As consequence of these results, we are able to determine growth envelopes of spaces B p,r and to show that we cannot describe all local embedding...