Exact(60)
Concerning regularity, we are able to prove interior W2,2α regularity results; concerning the boundary condition we consider both irregular and regular boundaries.
For regularity results, refer to Yuan [8] and Gala [9].
There are some previous partial regularity results for quasilinear systems.
Moreover, we achieve some regularity results of the solution.
Besides, the following boundary regularity results are well known.
Furthermore, some regularity results for the Dirichlet problem are obtained.
The regularity results are established via a blow-up argument.
For the n-switching problem we obtain regularity results for the solutions of the variational inequalities.
Therefore some additional assumptions on the coefficients is needed to ensure the regularity results.
In this section, we give a proof of partial regularity results.
In particular, it uses indirectly the very deep regularity results for parabolic PDEs.
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