It is known that if u∈BV the following inequality holds |Du_∏|(IR^n)≤|Du|( IR^n) where u_∏ is the polar rearrangement of u with respect to the hyperplane ∏ = {y= 0} and |Du|( IR^n), Du_∏|(IR^n) denote the total variation of u and u_∏ respectively. Moreover strict inequality may actually occur. In this paper we evaluate explicitely the difference |Du|(IR^n)- |D u_∏|(IR^n) and characterize those BV functions for which in the previous inequality strict inequality holds.
Functions of bounded variations and polarization / A., Alberico; A., Ferone; Volpicelli, Roberta. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - STAMPA. - 282:7(2009), pp. 953-963. [10.1002/mana.200710782]
Functions of bounded variations and polarization
VOLPICELLI, ROBERTA
2009
Abstract
It is known that if u∈BV the following inequality holds |Du_∏|(IR^n)≤|Du|( IR^n) where u_∏ is the polar rearrangement of u with respect to the hyperplane ∏ = {y= 0} and |Du|( IR^n), Du_∏|(IR^n) denote the total variation of u and u_∏ respectively. Moreover strict inequality may actually occur. In this paper we evaluate explicitely the difference |Du|(IR^n)- |D u_∏|(IR^n) and characterize those BV functions for which in the previous inequality strict inequality holds.| File | Dimensione | Formato | |
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