Abstract
For vector valued solutions \(u\) to the \(p\)-Laplacian system \(-\triangle _p u=F\) in a domain of \({\mathbb {R}}^n,\,p>1,\,n \ge 2,\) if \(F\) belongs to the limiting Lorentz space \(L(n,1),\) then \(Du\) is continuous.
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Communicated by N. Trudinger.
To Bernard Dacorogna on his 60th birthday.
The authors are supported by the ERC Grant 207573 “Vectorial Problems” and by the Academy of Finland project “Regularity theory for nonlinear parabolic partial differential equations”. The authors also thank Paolo Baroni and Neil Trudinger for remarks on a preliminary version of the paper.