AbstractIn this paper, we give a priori estimates near the boundary for solutions of a degenerate elliptic problems in the general Besov-type spaces $B_{p,q}^{s,\tau }$, containing as special cases: Goldberg space bmo, local Morrey-Campanato spaces l2,λ and the classical Hölder and Besov spaces $B_{p,q}^s $. This work extends the results of [13, 2, 15] from Hölder and Besov spaces to the general frame of $B_{p,q}^{s,\tau }$ spaces.
Abstract
In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.
The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.