Codice  QDD 164 
Titolo  Existence results for a fourth order partial differential equation arising in condensed matter physics 
Data  20131031 
Autore/i  Escudero, C.; Gazzola, F.; Hakl, R.; Peral I.; Torres P.J. 
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Abstract  We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initialboundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of selfsimilar solutions. 
