Loading [MathJax]/extensions/MathZoom.js
For , let be a bounded smooth domain and a compact smooth Riemannian manifold without boundary. Suppose that is a sequence of weak solutions in the critical dimension to the perturbed -polyharmonic maps
with in and weakly in . Then is an -polyharmonic map. In particular, the space of -polyharmonic maps is sequentially compact for the weak- topology.
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension , with data in . We also present related results concerning
differential forms with coefficients in the limiting Sobolev space .
We obtain sufficient conditions for nonexistence of nontrivial solutions for some classes of nonlinear partial differential inequalities containing the fractional powers of the Laplace operator.
We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.
Currently displaying 1 –
6 of
6