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Some results on the Jacobian equation with integrable data and a nonlinear open mapping principle

  • Lukas Koch (University of Oxford)
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Abstract

I will present results on the Jacobian equation det Du = f where f\in L^p. In particular, I will present results on generic non-existence of solutions on bounded domains as well as results on symmetry properties of the solution answering questions by Ye, Hogan-McIntosh-Zhang and Hélein. An important tool will be a nonlinear open mapping principle that is of independent interest. In fact, as an application of this principle I will show that the set of initial data for which there are dissipative weak solutions in L^p_t L^2_x of the incompressible Euler equations is meagre in the space of solenoidal L^2 fields.

Upcoming Events of this Seminar

  • Monday, 14.07.25 tba with Alexandra Holzinger
  • Tuesday, 15.07.25 tba with Anna Shalova
  • Friday, 15.08.25 tba with Thomas Suchanek
  • Friday, 22.08.25 tba with Nikolay Barashkov
  • Friday, 29.08.25 tba with Andreas Koller