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{\Large המחלקה למתמטיקה, בן-גוריון}

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{\Huge קולוקוויום}\\[0.2\baselineskip]

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\textbf{ב}\emph{יום שלישי, 20 ביוני, 2017}
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\textbf{בשעה} \emph{14:30 -- 15:30}
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\textbf{ב}\emph{Math -101}

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ההרצאה

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{\Large\bfseries Jumps detection in Besov spaces via a new BBM formula. Applications to Aviles-Giga type functionals\par}
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תינתן על-ידי
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{\large\scshape Arkady Poliakovsky 
  %
  (BGU)
}
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\textbf{תקציר:}
  Motivated by the formula, due to Bourgain, Brezis and Mironescu,
$\lim_{\varepsilon\to 0^+} \int_\Omega\int_\Omega
\frac{|u(x)-u(y)|^q}{|x-y|^q}\,\rho_{\varepsilon}(x-y)\,dx\,dy=K_{q,N}\|\nabla
u\|_{L^{q}}^q\,,$
that characterizes the functions in $L^q$ that belong to $W^{1,q}$
(for $q>1$) and $BV$ (for $q=1$), respectively, we study what
happens when one replaces the denominator in the expression above by
$|x-y|$. It turns out that, for $q>1$ the corresponding functionals
''see`{}` only the jumps of the $BV$ function. We further identify the
function space relevant to the study of these functionals, the space $BV^q$, as the
Besov space $B^{1/q}_{q,\infty}$. We show, among
other things, that $BV^q(\Omega)$ contains both the spaces
$BV(\Omega)\cap L^\infty(\Omega)$ and $W^{1/q,q}(\Omega)$. We also
present applications to the study of singular
perturbation problems of Aviles-Giga type.
  


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