Ruichang Pei1, 2 1 Center for Nonlinear Studies, Northwest University, Xi’an 710069, China 2 Department of Mathematics, Tianshui Normal University, Tianshui 741001, China Correspondence should be addressed to Ruichang Pei, [email protected] Received 26 February 2010; Revised 2 April 2010; Accepted 22 April 2010 Academic Editor: Kanishka Perera Copyright q 2010 Ruichang Pei. This is an open access ...

Optimal pointwise estimates are derived for the biharmonic Green function in arbitrary C4,γ -smooth domains. Maximum principles do not exist for fourth order elliptic equations and the Green function may change sign. It prevents using a Harnack inequality as for second order problems and hence complicates the derivation of optimal estimates. The present estimate is obtained by an asymptotic ana...

In this paper, we consider the well-posedness of inhomogeneous nonlinear biharmonic Schrödinger equation with spatial inhomogeneity coefficient K(x) behaves like |x|−b for 0<b<min⁡{N2,4}. We show local in whole Hs-subcritical case, 0<s≤2. The difficulties problem come from singularity and lack differentiability term. To resolve this, derive bilinear Strichartz's type estimates equations Besov s...

This paper considers an inverse boundary value problem associated to the Stokes equations which govern the motion of slow viscous incompressible ows of uids. The determination of the under-speci ed boundary values of the normal uid velocity is made possible by utilising within the analysis additional pressure measurements which are available from elsewhere on the boundary. The inverse boundary ...

The solution of the equations governing the two-dimensional slow viscous fluid flow is analysed using a novel technique based on a Laplacian decomposition instead of the more traditional approaches based on the biharmonic streamfunction formulation or the velocity-pressure formulation. This results in the need to solve three Laplace equations for the pressure and two auxiliary harmonic function...

Let T be a tree rooted at e endowed with a nearest-neighbor transition probability that yields a recurrent random walk. We show that there exists a function K biharmonic off e whose Laplacian has potential theoretic importance and, in addition, has the following property: Any function f on T which is biharmonic outside a finite set has a representation, unique up to addition of a harmonic funct...

SUMMARY Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method ' used in con junction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than...

We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.

In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature submanifolds in spheres.