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...

This paper presents an optimal solver for the Morley element problem for the boundaryvalue problem of the biharmonic equation by decomposing it into several subproblems and solving these subproblems optimally. The optimality of the proposed method is mathematically proved for general shape-regular grids. Mathematics subject classification: 65F08, 65N30, 65N99

In this paper, we are interested in some aspects of the biharmonic equation in the half-space R+ , with N ≥ 2. We study the regularity of generalized solutions in weighted Sobolev spaces, then we consider the question of singular boundary conditions. To finish, we envisage other sorts of boundary conditions.

We consider the inhomogeneous biharmonic nonlinear Schrödinger equation iut+?2u+?|x|?b|u|?u=0,where ?=±1 and ?, b>0. In subctritical case, we improve global well-posedness result obtained in Guzmán Pastor (2020) for dimensions N=5,6,7 Sobolev space H2(RN). The fundamental tools to establish our results are standard Strichartz estimates related linear problem Hardy-Littlewood inequality. Results...