Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions
A longstanding conjecture in elliptic regularity theory inquires whether a |$W^{1,p}$| function whose |$p$|-laplacian is bounded is locally of class |$C^{1,\frac{1}{p-1}}$|. While it is well known that such functions are of class |$C^{1,\alpha}$| for some unknown |$0<\alpha<1$|, establishing the sharp estimate turns out to be a rather delicate problem. Quite …