Elliptic systems of higher order with critical nonlinearity

• Applicant: Professor Dr. Andreas Gastel
• Subject Area: Mathematics
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 262992434

The regularity theory for weak solutions of quasilinear elliptic systems of second or fourth order with critical nonlinearity has been pushed to new levels in recent work by Rivière, Struwe, and Lamm. A similarly general theory for systems of higher order (in divergence form) is still lacking. In our project, we would like to start it with considering the problem in the critical dimension. This will probably involve the methods mentioned, combined with arguments which allow handling the Sobolev spaces of negative differentiability that are expected to occur.

• DFG Programme: Research Grants