Doctoral Dissertation

24.8.2018 M.Sc. Shirsho Mukherjee (Facul­ty of Mat­hema­tics and Science, Mathematics)


24.8.2018 13:00 — 16:00

Location: Mattilanniemi , MaA211
M.Sc. Shirsho Mukherjee defends his doctoral dissertation in Mathematics "Regularity of quasilinear sub-elliptic equations in the Heisenberg Group".

Opponent professor  Alexandru Kristaly (Babeș-Bolyai University, Romania) and Custos Professor Pekka Koskela (University of Jyväskylä). The doctoral dissertation is held in English.

This dissertation is about the regularity of solutions of certain quasilinear partial differential equations, so called sub-elliptic equations, which first appeared in the work of Hörmander in mid 60's. The equations have been considered in the setting of Heisenberg Groups. The main goal of the dissertation is to establish that the regularity theory for quasilinear sub-elliptic equations in the Heisenberg Group is the same as the classical regularity theory for quasilinear elliptic equations which underwent a longstanding development since the work of De Giorgi and Nash. The work of Mukherjee provides a complete comprehensive resolution to the regularity problem for such equations, which has been previously rendered incomplete in the last few decades.