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SUMMARY:Michał Miśkiewicz (Institute of Mathematics\, Polish Academy of 
 Sciences)
DTSTART:20220405T160000Z
DTEND:20220405T170000Z
DTSTAMP:20260423T035036Z
UID:OSGA/105
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/105/">S
 truggles with the regularity of $n$-harmonic maps</a>\nby Michał Miśkiew
 icz (Institute of Mathematics\, Polish Academy of Sciences) as part of Onl
 ine Seminar "Geometric Analysis"\n\n\nAbstract\nLet us consider the Dirich
 let $n$-energy $\\int_{\\mathcal{M}} |\\nabla u|^n$ for maps $u \\colon \\
 mathcal{M}^n \\to \\mathcal{N}^m$ between two Riemannian manifolds. Its Eu
 ler-Lagrange system – known as the $n$-harmonic equation – is an examp
 le of a conformally invariant system with critical nonlinearity. In genera
 l such systems can have discontinuous solutions\, but the regularity of $n
 $-harmonic maps is an open problem for $n > 2$. \n\nPartial results in thi
 s direction rely on the jacobian structure of the $n$-harmonic equation\, 
 together with the theory of Hardy and BMO spaces. After a brief review of 
 these methods\, I will describe a new application\, which leads to yet ano
 ther partial result – regularity for $W^{n/2\,2}$-solutions – but also
  gives some hope for further progress. \n\nThis is joint work with Paweł 
 Strzelecki and Bogdan Petraszczuk.\n
LOCATION:https://researchseminars.org/talk/OSGA/105/
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