Regularity of Evolutionary Problems via Harmonic Analysis and Operator Theory

• Applicant: Professor Dr. Wolfgang Arendt
• Subject Area: Mathematics
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 263969954

The proposal consists of four closely related parts. A first project concerns operator-valued Fourier multipliers. Here the proof of the Marcinkiewicz (periodic case) and Mikhlin Multiplier Theorem on spaces with Muckenhoupt weights form our central goal. Further aims concern multipliers with respect to general Schauder decompositions with applications to the closedness-of-the-sum-problem. The second part is the development of a structure theory for maximal regularity where positivity plays an essential role. Wide open is still maximal regularity in the non-autonomous case to which the third part is devoted. It is strongly motivated by quasilinear parabolic problems. Finally, all results will be tested for elliptic operators with diverse boundary conditions, the last part of the proposal.

• DFG Programme: Research Grants
• International Connection: Finland
• Participating Person: Professor Tuomas Hytönen, Ph.D.