In general, higher order elliptic equations and boundary value problems like the biharmonic equation or the linear clamped plate boundary value problem do not enjoy neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being written ...

We show that a bilinear estimate for biharmonic functions in a Lipschitz domain Ω is equivalent to the solvability of the Dirichlet problem for the biharmonic equation in Ω. As a result, we prove that for any given bounded Lipschitz domain Ω in Rd and 1 < q < ∞, the solvability of the Lq Dirichlet problem for ∆2u = 0 in Ω with boundary data in WA(∂Ω) is equivalent to that of the Lp regularity p...

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...

Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular ...

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...