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UID:20250915T074119EDT-4129ul8vA7@132.216.98.100
DTSTAMP:20250915T114119Z
DESCRIPTION:\n	\n		\n			\n				\n					\n						\n							\n								\n									\n										\n											\n												✒️ TITRE / TITLE\n\n												Convex integration 
 for the Monge-Ampere system\n													\n													📄 RÉSUMÉ / ABSTRACT\n\n												The Monge-Ampere sys
 tem (MA) is the multi-dimensional version of the Monge-Ampere equation\, a
 rising from the prescribed curvature problem and closely related to the pr
 oblems of isometric immersions and the minimization of elastic energies of
  thin shells.\n													\n													In case of dimension d=2 and codimension k=1\, (MA) reduc
 es to the classical Monge-Ampere equation as the prescription of the Gauss
 ian curvature of a shallow surface in R^3\, whereas (MA) prescribes the fu
 ll Riemann curvature of a shallow d-dimensional manifold in R^{d+k}.\n													\n													(M
 A) takes its weak formulation\, called the Von Karman system (VK). When d=
  2\, k= 1\, (VK) arises in the theory of elasticity as the the Von Karman 
 stretching content a thin film.\n													\n													Closely related to (MA) and (VK) is the
  system (II) for an isometric immersion of the given d-dimensional Riemann
 ian metric into R^{d+k}. (II) yields (VK) when equating the leading order 
 terms along a perturbation of the Euclidean metric.\n													\n													This lecture will c
 oncern the ongoing study of existence\, regularity\, and multiplicity of s
 olutions to systems (MA)\, (VK)\, (II) through the method of convex integr
 ation\, building on the prior fundamental results due to Nash\, Kuiper\, K
 allen\, Borisov\, the more recent approach due to Conti\, Delellis and Sze
 kelyhidi\, and the parallel analysis of Cao\, Hirsch and Inauen.\n													\n													We wil
 l also explore relation to the scaling of the non-Euclidean energies of el
 astic deformations and the quantitative isometric immersion problem.\n\n												📍 
 LIEU / PLACE\n													Hybride - CRM\, Salle / Room 5340\, Pavillon André Aisenstad
 t\n\n												 \n											\n										\n									\n								\n							\n						\n					\n				\n			\n		\n	\n\n\n \n\n\n	\n		\n			\n				\n					\n						\n							\n								Lien ZOOM Link\n							\n						
 \n					\n				\n			\n		\n	\n\n
DTSTART:20250905T193000Z
DTEND:20250905T203000Z
SUMMARY:Marta Lewicka (University of Pittsburgh)
URL:/mathstat/channels/event/marta-lewicka-university-
 pittsburgh-366967
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