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UID:1933@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171010T140000
DTEND;TZID=Europe/Paris:20171010T160000
DTSTAMP:20241209T221412Z
URL:https://www.i2m.univ-amu.fr/evenements/positivity-and-qualitative-prop
 erties-of-solutions-of-fourth-order-elliptic-equations/
SUMMARY:Giulio Romani (I2M\, Aix-Marseille Université): Positivity and qua
 litative properties of solutions of fourth-order elliptic equations
DESCRIPTION:Giulio Romani: This thesis concerns the study of fourth-order e
 lliptic boundary value problems and\, in particular\, qualitative properti
 es of solutions. Such problems arise in various fields\, from plate theory
  to conformal geometry and\, compared to their second-order counterparts\,
  they present intrinsic difficulties\, mainly due to the lack of the maxim
 um principle.\nIn the first part of the thesis\, we study the positivity o
 f solutions in case of Steklov boundary conditions\, which are intermediat
 e between Dirichlet and Navier boundary conditions. They naturally appear 
 in the study of the minimizers of the Kirchhoff-Love functional\, which re
 presents the energy of a hinged thin and loaded plate in dependence of a p
 arameter. We establish sufficient conditions on the domain to obtain the p
 ositivity of the minimizers of the functional. Then\, for such domains\, w
 e study a generalized version of the functional. Using variational techniq
 ues\, we investigate existence and positivity of the ground states\, as we
 ll as their asymptotic behaviour for the relevant values of the parameter.
 \nIn the second part of the thesis we establish uniform a-priori bounds fo
 r a class of fourth-order semilinear problems in dimension 4 with exponent
 ial nonlinearities. We considered both Dirichlet and Navier boundary condi
 tions and we suppose our nonlinearities positive and subcritical. Our argu
 ments combine uniform estimates near the boundary and a blow-up analysis. 
 Finally\, by means of the degree theory\, we obtain the existence of a pos
 itive solution.\n*Membres du jury :\n- François Hamel\, Aix-Marseille Uni
 versité (Directeur)\n- Enea Parini\, Aix-Marseille Université (Directeur
 )\n- Bernhard Ruf\, Università degli Studi di Milano (Co-Directeur)\n- Fi
 lippo Gazzola\, Politecnico di Milano (Rapporteur)\n- Frédéric Robert\, 
 Université de Lorraine (Rapporteur)\n- Elvise Berchio\, Politecnico di To
 rino (Examinatrice)\n- Anna Dall'Acqua\, Universität Ulm (Examinatrice)\n
 - Louis Dupaigne\, Université de Lyon 1 (Examinateur)\n\nLien : theses.fr
 \n-
CATEGORIES:Soutenance de thèse,Analyse Appliquée
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DTSTART:20170326T030000
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