Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence

@article{Mielke2020ExploringFO,
  title={Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence},
  author={Alexander Mielke and Alberto Montefusco and Mark A. Peletier},
  journal={arXiv: Functional Analysis},
  year={2020}
}
We introduce two new concepts of convergence of gradient systems $(\mathbf Q, \mathcal E_\varepsilon,\mathcal R_\varepsilon)$ to a limiting gradient system $(\mathbf Q, \mathcal E_0,\mathcal R_0)$. These new concepts are called `EDP convergence with tilting' and `contact--EDP convergence with tilting'. Both are based on the Energy-Dissipation-Principle (EDP) formulation of solutions of gradient systems, and can be seen as refinements of the Gamma-convergence for gradient flows first introduced… 
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