The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial progress has also been made for the polyhedral domains and domains with Lipschitz boundaries. However, very little is known about higher order elliptic equations in the general setting. In this paper we introduce new integral identities that allow to investigate the sol...

background: pentoxifylline (px) is a methyl xanthine derivative that influences the sperm motion characteristics and l-carnitine (l-c) is an amino acid that is naturally produced in the body. in general, separate administration of px and l-c has been reported to be effective on preserving sperm motility in vitro, and also when is consumed orally by the idiopathic oligoasthenoteratozoospermia (i...

Let X be a locally convex Hausdorff space (briefly, lcHs) and L(X) denote the space of all continuous linear operators of X into itself. The space L(X) is denoted by Ls(X) when it is equipped with the topology of pointwise convergence in X (i.e. the strong operator topology). By a spectral measure in X is meant a σ-additive map P : Σ → Ls(X), defined on a σ-algebra Σ of subsets of some set Ω, w...

In this paper, we study the Stokes system in the half-space R+, with n > 2. We consider data and give solutions which live in weighted Sobolev spaces, for a whole scale of weights. We start to study the kernels of the biharmonic and Stokes operators. After the central case of the generalized solutions, we are interested in strong solutions and symmetrically in very weak solutions by means of a ...

This work is devoted to study the existence and the regularity of solutions of two nonlinear problems of fourth order governed by p-biharmonic operators in nonresonance cases. In the first problem we establish the nonresonance part of the Fredholm alternative. In the second problem, nonresonance relative to the first eigenvalue is considered for p = 2 at the case where the nonresonance is betwe...

biharmonic surfaces in euclidean space $mathbb{e}^3$ are firstly studied from a differential geometric point of view by bang-yen chen, who showed that the only biharmonic surfaces are minimal ones. a surface $x : m^2rightarrowmathbb{e}^{3}$ is called biharmonic if $delta^2x=0$, where $delta$ is the laplace operator of $m^2$. we study the $l_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

We present a fast direct solver methodology for the Dirichlet biharmonic problem in a rectangle. The solver is applicable in the case of the second order Stephenson scheme [34] as well as in the case of a new fourth order scheme, which is discussed in this paper. It is based on the capacitance matrix method ([10], [8]). The discrete biharmonic operator is decomposed into two components. The fir...

In this paper we continue the study, which was initiated in (Ben-Artzi et al. in Math. Model. Numer. Anal. 35(2):313–303, 2001; Fishelov et al. in Lecture Notes in Computer Science, vol. 2667, pp. 809–817, 2003; Ben-Artzi et al. in J. Comput. Phys. 205(2):640–664, 2005 and SIAM J. Numer. Anal. 44(5):1997–2024, 2006) of the numerical resolution of the pure streamfunction formulation of the time-...

we investigate compact composition operators on ceratin lipschitzspaces of analytic functions on the closed unit disc of the plane.our approach also leads to some results about compositionoperators on zygmund type spaces.

OBJECTIVE Human T cell leukemia virus type I env-pX transgenic rats (env-pX rats) were used to investigate the pathogenesis of arthritis. METHODS Phenotype of cells infiltrated into arthritic joints in env-pX rats was analyzed using flow cytometry and cell-transfer experiments were done using env-pX and wild-type WKAH rats. RESULTS The majority of T cells infiltrated into arthritic joints i...