24 citations · 108 across the 16 of their papers we have counts for
19 papers
Decay of extremals of Morrey's inequality
Ryan Hynd, Simon Larson, Erik Lindgren
We study the decay (at infinity) of extremals of Morrey's inequality in . These are functions satisfying $$ \displaystyle \sup_{x\neq y}\frac{|u(x)-u(y)|}{|x-y|^{1-\f…
Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena
Pu-Zhao Kow, Simon Larson, Mikko Salo +1
In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We als…
An inequality for the normal derivative of the Lane-Emden ground state
Rupert L. Frank, Simon Larson
We consider Lane-Emden ground states with polytropic index , that is, minimizers of the Dirichlet integral among -normalized functions. Our main result is a s…
Discrete Schrödinger operators with decaying and oscillating potentials
Rupert L. Frank, Simon Larson
We study a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential $V(n)=λn^{-α}\cos(…
On the spectrum of the Kronig-Penney model in a constant electric field
Rupert L. Frank, Simon Larson
We are interested in the nature of the spectrum of the one-dimensional Schrödinger operator $$ - \frac{d^2}{dx^2}-Fx + \sum_{n \in \mathbb{Z}}g_n δ(x-n) \qquad\text{in } L^2(\mathb…
Two consequences of Davies's Hardy inequality
Rupert L. Frank, Simon Larson
In this short note we would like to show that one can use Davies's Hardy inequality to rederive well-known results of Lieb and Rozenblum.