We prove that a stationary extrinsic (or intrinsic, respectively) biharmonic map u 2 W ( ; N) from R into a Riemnanian manifold N is smooth away from a closed set of (m 4)-dimensional Hausdor measure zero. x

We study the regularity of solutions to the obstacle problem for the parabolic biharmonic equation. We analyze the problem via an implicit time discretization, and we prove some regularity properties of the solution.

This paper shows the existence of at least three solutions for Navier problem involving the p(x)-biharmonic operator. Our technical approach is based on a theorem obtained by B. Ricceri.

We consider additive Schwarz methods for the biharmonic Dirichlet problem and show that the algorithms have optimal convergence properties for some conforming nite elements. Some multilevel methods are also discussed.

It is shown that the Orlicz–Lorentz spaces $\ell ^n_{M,a}$, $n\in \mathbb {N}$, with Orlicz function $M$ and weight sequence $a$ are uniformly isomorphic to subspaces of $L_1$ if norm $\| \cdot \|_{M,a}$ satisfies certain Hardy-type inequalities. This includes embedding some Lorentz $\mathrm {d}^n(a,p)$. The approach based on combinatorial averaging techniques, a new result independent intere...

New representations of solutions Lamé system with real coefficients via monogenic functions in the biharmonic algebra are found.