15 citations · 45 across the 40 of their papers we have counts for
6 papers · 2 filters
Approximating Pointwise Products of Laplacian Eigenfunctions
Jianfeng Lu, Christopher D. Sogge, Stefan Steinerberger
We consider Laplacian eigenfunctions on a dimensional bounded domain (or a dimensional compact manifold ) with Dirichlet conditions. These operators give rise to a s…
A Nonlocal Transport Equation Describing Roots of Polynomials Under Differentiation
Stefan Steinerberger
Let be a polynomial of degree having all its roots on the real line distributed according to a smooth function . One could wonder how the distribution of roots be…
Quantitative Homogenization and Convergence of Moving Averages
Stefan Steinerberger
We study homogenization it its most basic form $$-\left(a\left(\frac{x}{\varepsilon}\right) u_{\varepsilon}'(x)\right)' = f(x) \quad \mbox{for} ~x \in (0,1),$$ where is…
Localization of Neumann Eigenfunctions near Irregular Boundaries
Peter W. Jones, Stefan Steinerberger
It has been empirically observed that eigenfunctions of Laplace's equation with Neumann boundary conditions sometimes localize near the boundary of the domain if that bou…
A Metric Sturm-Liouville theory in Two Dimensions
Stefan Steinerberger
A central result of Sturm-Liouville theory (also called the Sturm-Hurwitz Theorem) states that if is a sequence of eigenfunctions of a second order differential operator on t…
An Endpoint Alexandrov Bakelman Pucci Estimate in the Plane
Stefan Steinerberger
The classical Alexandrov-Bakelman-Pucci estimate for the Laplacian states $$ \max_{x \in Ω}{ |u(x)|} \leq \max_{x \in \partial Ω}{|u(x)|} + c_{s,n} \mbox{diam}(Ω)^{2-\frac{n}{s}} \…