33 citations · 53 across the 8 of their papers we have counts for
12 papers
Pólya's conjecture fails for the fractional Laplacian
Mateusz Kwaśnicki, Richard S. Laugesen, Bartłomiej A. Siudeja
The analogue of Pólya's conjecture is shown to fail for the fractional Laplacian (-Delta)^{alpha/2} on an interval in 1-dimension, whenever 0 < alpha < 2. The failure is total: eve…
Torsion and ground state maxima: close but not the same
Brian A. Benson, Richard S. Laugesen, Michael Minion +1
Could the location of the maximum point for a positive solution of a semilinear Poisson equation on a convex domain be independent of the form of the nonlinearity? Cima and Derrick…
Trace estimates for unimodal Lévy processes
Krzysztof Bogdan, Bartłomiej A. Siudeja
We give two-term small-time approximation for the trace of the Dirichlet heat kernel of bounded smooth domain for unimodal Lévy processes satisfying the weak scaling conditions.
Steklov eigenvalues and quasiconformal maps of simply connected planar domains
A. Girouard, R. S. Laugesen, B. A. Siudeja
We investigate isoperimetric upper bounds for sums of consecutive Steklov eigenvalues of planar domains. The normalization involves the perimeter and scale-invariant geometric fact…
Martin kernel for fractional Laplacian in narrow cones
Krzysztof Bogdan, Bartłomiej Siudeja, Andrzej Stós
We give a power law for the homogeneity degree of the Martin kernel of the fractional Laplacian for the right circular cone when the angle of the cone tends to zero.
Magnetic spectral bounds on starlike plane domains
R. S. Laugesen, B. A. Siudeja
We develop sharp upper bounds for energy levels of the magnetic Laplacian on starlike plane domains, under either Dirichlet or Neumann boundary conditions and assuming a constant m…