On the global regularity for nonlinear systems of the p-Laplacian type

Details On the global regularity for nonlinear systems of the p-Laplacian type On the global regularity for nonlinear systems of the p-Laplacian type

2010-08-19

arxiv.org/abs/1008.3262v3

Mathematics

Analysis of PDEs

This is a revised version of a previous one, online from 19 Aug 2010. We essentially weaken the assumptions of Theorem 2.3

Scientific paper

We consider the Dirichlet boundary value problem for nonlinear systems of partial differential equations with p-structure. We choose two representative cases: the "full gradient case", corresponding to a p-Laplacian, and the "symmetric gradient case", arising from mathematical physics. The domain is either the "cubic domain" (see the definition below) or a bounded open subset of R^3 with a smooth boundary. We are interested in regularity results, up to the boundary, for the second order derivatives of the velocity field. Depending on the model and on the range of p, p<2 or p>2, we prove different regularity results. It is worth noting that in the full gradient case with p<2 we cover the degenerate case and obtain W^{2,q}-global regularity results, for arbitrarily large values of q.

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