We consider the Steklov problem for the linear biharmonic equation. We survey existing results for the positivity preserving property to hold. These are connected with the first Steklov eigenvalue. We address the problem of minimizing this eigenvalue among suitable classes of domains. We prove the existence of an optimal convex domain of fixed measure. Mathematics Subject Classification (2000)....

We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equation ∆ 2 u = |u| p in a ball with p > 0.

A tensor-product Bézier surface patch x of degree (m,n) is called biharmonic if it satisfies 2x = 0. As shown by Monterde and Ugail (2004), these surface patches are fully determined by their four boundaries. In this note we derive necessary conditions for their existence. © 2006 Elsevier B.V. All rights reserved.

In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for generalized stable maps.