For a p-curl system in a bounded convex domain, weak solutions exist uniquely and their curl lies in L∞, with the bound ‖curl u‖_{L∞} ≤ C‖f‖_{L^{3,1}}^{1/(p-1)}.
Yin, Regularity of weak solution to an p-curl syste m, Differ
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Global boundedness of the curl for a p-curl system in convex domains
For a p-curl system in a bounded convex domain, weak solutions exist uniquely and their curl lies in L∞, with the bound ‖curl u‖_{L∞} ≤ C‖f‖_{L^{3,1}}^{1/(p-1)}.