Wang, T. (2012). The affine Sobolev–Zhang inequality on BV(ℝn). Advances in Mathematics, 230(4–6), 2457–2473. https://doi.org/10.1016/j.aim.2012.04.022
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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Zeitschrift:
Advances in Mathematics
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ISSN:
0001-8708
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Datum (veröffentlicht):
2012
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Umfang:
17
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Verlag:
ACADEMIC PRESS INC ELSEVIER SCIENCE
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Peer Reviewed:
Ja
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Keywords:
General Mathematics; Sets of finite perimeter; The affine Sobolev–Zhang inequality; The Petty projection ienquality
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Abstract:
The affine Sobolev–Zhang inequality is extended to BV(ℝⁿ), the space of functions of bounded variation on ℝⁿ , and the equality cases are characterized. As a consequence, the Petty projection inequality for sets of finite perimeter, which implies the isoperimetric inequality for sets of finite perimeter, is established.
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Forschungsschwerpunkte:
außerhalb der gesamtuniversitären Forschungsschwerpunkte: 100%
