Current Position
Current Position
I am a Maître de Conference (Associated Professor) at Sorbonne Université - Laboratoire Jacques-Louis Lions
You can find my complete cv here.
Email: nikita.simonov(at)sorbonne-universite.fr
Research Interests
Regularity of Linear and Nonlinear Parabolic PDEs of Singular/Degenerate type: how the degeneracy/singularity of the coefficients affects the regularity of the solution. Especially in Fast Diffusion Equation, Porous Medium Equation (with or without weights).
Asymptotic behavior of solutions to Parabolic PDEs: rate of convergence to an equilibrium state, quantitative information about fine properties of the solutions.
Functional inequalities (Sobolev, Gagliardo-Nirenberg, Poincaré Inequality) and their relations with nonlinear flows.