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SEMINARS |
V. I. Smirnov Seminar on Mathematical Physics
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Existence of planar H-loops via Hardy's inequality R. Musina University of Udine |
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Abstract: Given a continuous function on \begin{equation} \label{eq:problem} u''=|u'|~\!{\rm H}(u) iu'. \end{equation} Any non-constant solution to \eqref{eq:problem} parametrizes a closed planar curve having prescribed curvature Problem \eqref{eq:problem} admits a variational formulation; under reasonable assumptions on the prescribed (non-constant) curvature We will present an existence result which is strongly based on a Hardy type inequality for functions of two variables. This is joint work with Gabriele Cora (Università di Torino, Italy). Language: English |