Real varieties and measure-valued solutions to PDEs
- Jonas Hirsch (Leipzig University)
Measure valued solutions to constant coefficient PDEs appear natural in calculus of variations. For instance they can be used characterise gradients, symmetric gradients or appear in the Euler-Lagrange equations of geometric variational problems. In this talk I discuss how the wave cone -- the real variety determined by the kernel of the associated polynomial matrices -- gives structural conditions on the “size” and “directions” of the singular part of the measure. For instance we can conclude in certain situations the rectifiability of the “lowest density” part of the measure.