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DTSTART;TZID=Europe/Berlin:20230316T141500
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SUMMARY:Oberseminar Analysis - Prof. Dr. Marta Lewicka (University of Pittsburgh)
DESCRIPTION:Title: The Monge-Ampere system: flexibility in arbitrary dimension and codimension\n\nAbstract: \n\nIn this talk\, we will be concerned with weak solutions obtained by means of convex integration\, to the Monge-Ampere system. This system is a natural extension of the Monge-Ampere equation $\\det\\nabla^2 v=f$ in dimension d=2\, to the linearization of the full Riemann curvature tensor in arbitrary dimension d\, and arises in relation to:\n(i) the problem of existence of isometric immersions and\n(ii) the context of nonlinear elasticity.\n\nOur main technical ingredient consists of the "stage" construction\, in which we achieve the Hölder regularity $\\mathcal{C}^{1\,\\alpha}$ of solutions to the aforementioned system\, approximating its any subsolution\, with exponents $\\alpha<\\frac{1}{1+ d(d+1)/k}$ where d is an arbitrary dimension and $k\\geq 1$ is an arbitrary codimension in the problem.\n\nWhen d=2 and k=1\, we recover the previous result by Lewicka-Pakzad for the Monge-Ampere equation. Our construction can be translated to the isometric immersion problem\, where for k=1 we recover the result by Conti-Delellis-Szekelyhidi\, and for large k we quantify the result by Kallen.
LOCATION:Endenicher Allee 60
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