Matias Vestberg's Research Page
I am a Ph.D. student at Aalto University School of Science, Department of Mathematics and Systems Analysis.
I am part of the Nonlinear PDE research group led by professor Juha Kinnunen who is also my supervisor.
My current research is concerned with regularity and existence of solutions to nonlinear parabolic PDEs.
V. Bögelein, N. Dietrich and M. Vestberg: Existence of solutions to a diffusive shallow medium equation. Submitted to a Journal, 35 pages, 2020. Available at: arXiv:2001.07942.
V. Vespri and M. Vestberg: An Extensive Study of the Regularity of Solutions to Doubly Singular equations. Accepted by Advances in Calculus of Variations, 2020. Available at: arXiv:2001.04141.
T. Singer, M. Vestberg: Local Hölder continuity of weak solutions to a diffusive shallow medium equation. Nonlinear Analysis, Vol. 185, 306-335, 2019. doi: 10.1016/j.na.2019.03.013
T. Singer, M. Vestberg: Local boundedness of weak solutions to the diffusive wave approximation of the shallow water equations, Journal of Differential Equations, Vol. 266 no. 6, 3014-3033, 2019. doi: 10.1016/j.jde.2018.08.051
Master's Thesis, The Wave Front Set and Oscillatory Integrals.
My website at the department
The Nonlinear PDE group website