In this paper we give an enclosure for the solution of the biharmonic problem and also for its gradient and Laplacian in the L2-norm, respectively.

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...

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...

fies the biharmonic equation. The detailed behavior of solutions to the biharmonic equation on regions with corners has been historically difficult to characterize. The problem was first examined by Lord Rayleigh in 1920; in 1973, the existence of infinite oscillations in the domain Green’s function was proven in the case of the right angle by S. Osher. In this paper, we observe that, when the ...

We are interested in entire solutions for the semilinear biharmonic equation ∆u = f(u) in R , where f(u) = e or −u−p (p > 0). For the exponential case, we prove that for the polyharmonic problem ∆u = e with positive integer m, any classical entire solution verifies ∆2m−1u < 0, this completes the results in [6, 14]; we obtain also a refined asymptotic expansion of radial separatrix solution to ∆...

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 first establish regularity of the heat flow of biharmonic maps into the unit sphere S ⊂ R under a smallness condition of renormalized total energy. For the class of such solutions to the heat flow of biharmonic maps, we prove the properties of uniqueness, convexity of hessian energy, and unique limit at t = ∞. We establish both regularity and uniqueness for Serrin’s (p, q)-sol...