Among various barycentric coordinates and their extensions, the linear and cubic (Hermite) Gordon-Wixom transfinite interpolation schemes deliver the most accurate approximations of the harmonic and biharmonic functions, respectively. However interpolation properties of the original Gordon-Wixom interpolations are studied for convex domains only and, therefore, their current practical importanc...

Abstract Using variational methods and critical point results, we prove the existence multiplicity of weak solutions a $(p(x),q(x))$ ( p x ) , q -biharmonic elliptic equation along with singular term under Navier boundary con...

The evaluation of sums (matrix–vector products) of the solutions of the three-dimensional biharmonic equation can be accelerated using the fast multipole method, while memory requirements can also be significantly reduced. We develop a complete translation theory for these equations. It is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering ...

In this paper, we establish the existence of at least two distinct weak solutions for some singular elliptic problems involving a p-biharmonic operator, subject to Navier boundary conditions in a smooth bounded domain in RN . A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least two distinct nontrivial weak solutions.

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...

In this paper, we study B-focal curves of biharmonic B -general helices according to Bishop frame in the Heisenberg group Heis   Finally, we characterize the B-focal curves of biharmonic B- general helices in terms of Bishop frame in the Heisenberg group Heis        

This manuscript discusses the existence of nontrivial weak solution for following nonlinear eigenvalue problem driven by p(?)-biharmonic operator with Rellich-type term {?(|?u|p(x)?2?u) = ?|u|q(x)?2u/?(x)2q(x), x ? ?, u ?u 0, ??. Considering case 1 &lt; min x?? p(x) max q(x) (N 2, Np(x) N 2p(x) ), we extend corresponding result reference [8], .p(x) 2 . The proofs main results are based on mount...

The biharmonic supercritical equation ∆u = |u|p−1u, where n > 4 and p > (n + 4)/(n − 4), is studied in the whole space R as well as in a modified form with λ(1 + u) as right-hand-side with an additional eigenvalue parameter λ > 0 in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions we prove oscillatory behaviour around the expl...

We consider a finite element method based on biorthogonal or quasi-biorthogonal systems for the biharmonic problem. The method is based on the primal mixed finite element method due to Ciarlet and Raviart for the biharmonic equation. Using different finite element spaces for the stream function and vorticity, this approach leads to a formulation only based on the stream function. We prove optim...