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Session 11. Geometric Analysis and Related Topics
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Conditional regularity for \(p\)-parabolic systems with critical right hand side
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Krystian Kazaniecki, University of Warsaw, Poland
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The talk is based on the joint work with Michał Łasica, Katarzyna Mazowiecka
and Paweł Strzelecki
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We prove an \(\varepsilon\)-regularity result for a wide class of parabolic systems
\[
u_t-\text{div}\big(|\nabla u|^{p-2}\nabla u) = B(u, \nabla u)
\]
with the right hand side \(B\) growing like \(|\nabla u|^p\). It is assumed that the solution \(u(t,\cdot)\) is uniformly small in the space of functions of bounded mean oscillation. The crucial tool is provided by a sharp nonlinear version of the Gagliardo-Nirenberg inequality which has been used earlier in an elliptic context by T. Rivière and P. Strzelecki.
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