University of Cambridge > Talks.cam > Cambridge Centre for Analysis talks > The positive Jacobian constraint in elasticity theory and orientation-preserving Young measures

  Browse A-Z

Log in

University Account External (via Google)

🔐 Log In

Information on

Subscribing to talksdetails Finding a talkdetails Adding a talkdetails Disseminating talksdetails Help and Documentationdetails

ℹī¸ Information

The positive Jacobian constraint in elasticity theory and orientation-preserving Young measures

Download to your calendar using vCal

  • UserDr Filip Rindler, University of Warwick Speaker website
  • ClockTuesday 13 October 2015, 14:00-18:00
  • HouseMR2.

If you have a question about this talk, please contact CCA .

In elasticity theory, one naturally requires that the Jacobian determinant of the deformation is positive or even a-priori prescribed (for example in the case of incompressibility). However, such strongly non-linear and non-convex constraints are difficult to deal with in mathematical models. In this minicourse, I will present various recent results on how this constraint can be manipulated in subcritical Sobolev spaces, where the integrability exponent is less than the dimension. This setting is related to cavitation and fracture phenomena in materials. In particular, after introducing the appropriate notions, I will present a characterization of such constraint on the Jacobian determinant formulated in the language of Young measures. These objects, which I will briefly introduce, are widely used in the Calculus of Variations to model limits of nonlinear functions of weakly converging “generating” sequences. I will also discuss relations to convex integration and “geometry” in matrix space. Finally, I will show some applications to the minimization of integral functionals, the theory of semiconvex hulls and incompressible extensions.

This talk is part of the Cambridge Centre for Analysis talks series.

This talk is included in these lists:

Note that ex-directory lists are not shown.

Other lists

Sir Arhur Marshall Room, Engineering Design Centre, CUED Computer Lab, FW11 and Online (zoom link below) Seminar Room 3, Cripps Court, Magdalene College

Other talks

Washing machines and their rare components: lessons from kidney patients Title to be confirmed LMB Seminar - Mechanisms of mRNA packaging and export Think Before you Speak: Next Gen LLMs with Global Reasoning and External Memory Market Failure, Organ Shortage, Pandemic and Climate Change: The Architecture of Cooperation Differences between Robin and Neumann eigenvalues
 

Š 2006-2025 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity