PDEA Seminar: On the asymptotics of a free boundary problem determined by the gradient

Abstract: In elastic plastic problems the transition from an elastic region to a plastic region can often be formulated as a free boundary problem depending on the gradient of the stress function. Inspired by this we consider a scalar minimization problem which gives rise to a free boundary that is given by the gradient of the minimizer. Unlike many other free boundary problems we are not able to use the gradient of the solution as a model of the normal of the free boundary. Instead we develop the third order asymptotics for the solution under standard flatness and non-degeneracy assumptions, and show how it can be used to model the normal to the free boundary.

Participate on site or via Zoom link, meeting ID: 67226102216

This is a seminar in the PDEs and Applications seminar series