A criterion for the continuity of weakly monotone functions is proposed in terms of the decreasing rearrangement of their gradient. Its use in the proof of the continuity of weakly monotone functions with gradient in rearrangement-invariant spaces is also demonstrated. In particular, weakly monotone functions whose gradient belongs to an Orlicz space or to a Lorentz space are discussed, and results available in the literature in this regard are extended and refined.
On the continuity of weakly monotone functions / Carozza M.; Cianchi A.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 177:(2018), pp. 238-253. [10.1016/j.na.2018.04.016]
On the continuity of weakly monotone functions
Cianchi A.
2018
Abstract
A criterion for the continuity of weakly monotone functions is proposed in terms of the decreasing rearrangement of their gradient. Its use in the proof of the continuity of weakly monotone functions with gradient in rearrangement-invariant spaces is also demonstrated. In particular, weakly monotone functions whose gradient belongs to an Orlicz space or to a Lorentz space are discussed, and results available in the literature in this regard are extended and refined.
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