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EnglishIt 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.
| Titolo: | Functions of bounded variations and polarization |
| Autori: | |
| Data di pubblicazione: | 2009 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11588/301502 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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