Abstract. Let Ω be a bounded Lipschitz domain in R. We develop a new approach to the invertibility on L(∂Ω) of the layer potentials associated with elliptic equations and systems in Ω. As a consequence, for n ≥ 4 and 2(n−1) n+1 − ε < p < 2 where ε > 0 depends on Ω, we obtain the solvability of the L Neumann type boundary value problems for second order elliptic systems. The analogous results fo...

The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new discrete second order partial derivative introduced in gWG scheme to allow arbitrary combinations of piecewise polynomial functions defined interior on boundary general polygonal or polyhedral elements. error estimates are established numerical approximation a H2 norm L2 norm. r...

Considering difference equations in discrete space instead of differential equations in Euclidean space, we investigate a probabilistic formula for the solution of the Dirichlet problem for biharmonic functions. This formula involves the expectation of a weighted sum of the pay-offs at the successive times at which the Markov chain is in the complement of the domain. To make the infinite sum co...

This is a supplement to our previous research note [3]. In [3], we gave a characterization of biharmonic curves in Minkowski 3-space. More precisely, we pointed out that every biharmonic curves with nonnull principal normal in Minkowski 3-space is a helix, whose curvature κ and torsion τ satisfy κ2 = τ2. In the classification of biharmonic curves in Minkowski 3-space due to Chen and Ishikawa [1...

Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like: θ θ 2 sin sin b a + . The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes unde...