G. Grubb

activity

20012026

most citedFractional Laplacians on domains, a development of Hörmander's theory of mu-transmission pseudodifferential operators

262 citations · 606 across the 33 of their papers we have counts for

collaborators

38 papers

math.AP2026

The structure of solution spaces for fractional-order operators, with gradient estimates

Gerd Grubb

The solution space of the homogeneous Dirichlet problem for the fractional Laplacian $(- Δ)^{a}$ ( $0 < a < 1$ ) or a pseudodifferential generalization $P$ , on a bounded open set $Ω\subse…

math.AP2022

Weyl asymptotics for fractional-order Dirichlet realizations in nonsmooth cases

Gerd Grubb

Let $P$ be a symmetric $2 a$ -order classical strongly elliptic pseudodifferential operator with even symbol $p (x, ξ)$ on $R^{n}$ ( $0 < a < 1$ ), for example a perturbation of $(- Δ)^{a}$ . Let…

math.AP2022★ 5 cited

Fourier methods for fractional-order operators

Gerd Grubb

This is a survey on the use of Fourier transformation methods in the treatment of boundary problems for the fractional Laplacian $(- Δ)^{a}$ (0<a<1), and pseudodifferential generaliza…

math.AP2021★ 9 cited

Resolvents for fractional-order operators with nonhomogeneous local boundary conditions

Gerd Grubb

For $2 a$ -order strongly elliptic operators $P$ generalizing $(- Δ)^{a}$ , $0 < a < 1$ , the treatment of the homogeneous Dirichlet problem on a bounded open set $Ω \subset R^{n}$ by pseudodiff…

math.AP2021★ 2 cited

The principal transmission condition

Gerd Grubb

The paper treats pseudodifferential operators $P = O p (p (ξ))$ with homogeneous complex symbol $p (ξ)$ of order $2 a > 0$ , generalizing the fractional Laplacian $(- Δ)^{a}$ but lacking its sy…

math.AP2020★ 4 cited

Integration by parts for nonsymmetric fractional-order operators on a halfspace

Gerd Grubb

For a strongly elliptic pseudodifferential operator $L$ of order $2 a$ ( $0 < a < 1$ ) with real kernel, we show an integration-by-parts formula for solutions of the homogeneous Dirichlet…