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BEGIN:VEVENT
UID:news492@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181229T225231
DTSTART;TZID=Europe/Zurich:20131127T151500
SUMMARY:Seminar Analysis: Nikolay Gusev (SISSA Trieste)
DESCRIPTION:Suppose that b:Rd→Rd is a vector field\,  β:R→R  is a smo
 th function and u:R2→R is a scalar field. If both u and b are  smooth th
 en the following formula holds: div(β(u))b = β(u) - (β'(u) - uβ'(u)) 
 div (b) + β'(u) div(ub). Generalizations of this formula when u∈L∞ an
 d b belongs to Sobolev space or has bounded variation were studied by R. D
 i  Perna\, P.-L. Lions\, L. Ambrosio\, C. De Lellis\, J. Maly and other  a
 uthors. I will present a new result in this direction for d=2\, which  was
  obtained recently in collaboration with S. Bianchini. In particular  our 
 result holds when b is steady nearly incompressible BV vector  field.
X-ALT-DESC:\nSuppose that b:<b>R</b><sup>d</sup><b>→R</b><sup>d</sup> is 
 a vector field\,  β:<b>R</b><b>→R</b><sup>&nbsp\;</sup> is a smoth func
 tion and u:<b>R</b><sup>2</sup><b>→R</b> is a scalar field. If both u an
 d b are  smooth then the following formula holds: div(β(u))b =&nbsp\;β(u
 ) - (β'(u) - uβ'(u)) div (b) + β'(u) div(ub). Generalizations of this f
 ormula when u∈L<sup>∞</sup> and b belongs to Sobolev space or has boun
 ded variation were studied by R. Di  Perna\, P.-L. Lions\, L. Ambrosio\, C
 . De Lellis\, J. Maly and other  authors. I will present a new result in t
 his direction for d=2\, which  was obtained recently in collaboration with
  S. Bianchini. In particular  our result holds when b is steady nearly inc
 ompressible BV vector  field.
DTEND;TZID=Europe/Zurich:20131127T161500
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