Stig Larsson

TL;DR: In this paper, the Hilbert space-valued Wiener process and the corresponding stochastic integral of Ito type were introduced and used together with semigroup theory to obtain existence and uniqueness of weak solutions of linear and semilinear stochiastic evolution problems in Hilbert space.

TL;DR: A Two-Point Boundary Value Problem with Finite Difference Methods for Elliptic Equations and Finite Element methods for Hyperbolic Equations.

TL;DR: In this article, a finite element method for the Cahn-Hilliard equation (a semilinear parabolic equation of fourth order) is analyzed, both in a spatially semidiscrete case and in a completely discrete case based on the backward Euler method.

TL;DR: The analysis presented allows variable time steps which, as will be shown, call then efficiently be selected to match singularities in the solution induced by singularity in the kernel of the memory term or by nonsmooth initial data.

TL;DR: In this paper, a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise is considered, and a method of identifying the posterior using its precision operator is presented, which enables to use partial differential equations (PDE) methodology to obtain rates of contraction of the posterior distribution to a Dirac measure centered on the true solution.