40 citations · 50 across the 8 of their papers we have counts for
10 papers · 1 filter
An Introduction to the Obstacle Problem
Andreas Minne
We give a self-contained account of the classical obstacle problem, written for graduate students who wish to enter the field of free boundary problems. Starting from a one-dimensi…
Fully nonlinear free boundary problems: optimal boundary regularity beyond convexity
Damião J. Araújo, Andreas Minne, Edgard A. Pimentel
We study a general class of elliptic free boundary problems equipped with a Dirichlet boundary condition. Our primary result establishes an optimal -regularity estimate fo…
Symmetrized and non-symmetrized Asymptotic Mean Value Laplacian in metric measure spaces
Andreas Minne, David Tewodrose
The asymptotic mean value Laplacian - AMV Laplacian - extends the Laplace operator from to metric measure spaces through limits of averaging integrals. The AMV Lapla…
Asymptotic Mean Value Laplacian in Metric Measure Spaces
Andreas Minne, David Tewodrose
We use the mean value property in an asymptotic way to provide a notion of a pointwise Laplacian, called AMV Laplacian, that we study in several contexts including the Heisenberg g…
Optimal Regularity of Solutions to No-Sign Obstacle-Type Problems for the Sub-Laplacian
Valentino Magnani, Andreas Minne
We establish the optimal interior regularity of solutions to \[ Δ_{H}u=fχ_{\{u\ne0\}}, \] where denotes the sub-Laplacian operator in a stratified group. We a…
Regularity of solutions in semilinear elliptic theory
Emanuel Indrei, Andreas Minne, Levon Nurbekyan
We study the semilinear Poisson equation \begin{equation} \label{pro} Δu = f(x, u) \hskip .2 in \text{in} \hskip .2 in B_1. \end{equation} Our main results provide conditions on $f…
Classification of Blow-ups and Free Boundaries of Solutions to Unstable Free Boundary Problems
Andreas Minne
In general, solutions to \[ Δu(\mathbf{x})=f(\mathbf{x})χ_{\{u>ψ\}} \] are not , even for smooth and . Points around which is not $C^{1,1…
Non-transversal intersection of free and fixed boundary for fully nonlinear elliptic operators in two dimensions
Emanuel Indrei, Andreas Minne
In the study of classical obstacle problems, it is well known that in many configurations the free boundary intersects the fixed boundary tangentially. The arguments involved in pr…
Viscosity Solutions of Balanced Quasi-Monotone Fully Nonlinear Weakly Coupled Systems
Andreas Minne, Martin H. Strömqvist
We introduce so called balanced quasi-monotone systems. These are systems , where belongs to a domain , $r=u(x)\in\mathbb{R}^m…
Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems
Emanuel Indrei, Andreas Minne
We consider fully nonlinear obstacle-type problems of the form \begin{equation*} \begin{cases} F(D^{2}u,x)=f(x) & \text{a.e. in}B_{1}\capΩ,|D^{2}u|\le K & \text{a.e. in}B_{1}\backs…