Research

Research Interests

  • Theory of Partial Differential Equations
  • Calculus of Variations
  • Elliptic and parabolic (quasi-)minimizers
  • PDE with non-standard growth conditions
  • (Parabolic) quasiminimizers on metric measure spaces

Projects

Term: 01-05-2020 - 30-06-2022
Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)

The subproject ist concerned with stability questions for the non stationary gas flow in gas networks, which is described by the friction dominated ISO-3 model. From the analytical point of view the model consists in a system of nonlinear parabolic partial differential equations which can be transformed into a doubly nonlinear degenerate parabolic equation. We focus on stability issues for the (weak) solution (in the parabolic Sobolev space) with respect to variations of structural parameters and initial-boundary data. In particular, we expect results for the ISO-3 model concerning the stability under variations of friction parameters and the underlying gas model (ideal or real gas).

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Term: 01-01-2015 - 31-12-2019
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:

The aim of this project is to make a substantial contrubution to existence and regularity theory for solutions of nonlinear parabolic minimization problems on general metric measure spaces. It is intended to establish a systematic approach to the generalization of a result by A. Grigor'yan and L. Saloff-Coste on the relation between solutions of the heat equation on Riemannian manifolds and the validity of Harnack estimates. The interest is to generalize this result in two ways: Firstly, one…

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