Work

Functional calculus on weighted Sobolev spaces for the Laplacian on rough domains

Year: 2025

Type: article

Abstract: We study the Laplace operator on domains subject to Dirichlet or Neumann boundary conditions. We show that these operators admit a bounded $H^{\infty}$-functional calculus on weighted Sobolev spaces, where the weights are powers of the distance to the boundary. Our analysis applies to bounded $C^{1,λ}$-domains with $λ\in[0,1]$, revealing a crucial trade-off: lower domain regularity can be compensated by enlarging the weight exponent. As a primary consequence, we establish maximal regularity for the corresponding heat equation. This extends the well-posedness theory for parabolic equations to domains with minimal smoothness, where classical methods are inapplicable.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113884

Authors: Nick Lindemulder, Emiel Lorist, Floris B. Roodenburg, Mark C. Veraar

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Academy of Finland, Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Awards: G1749444191, Mathematical analysis of quasilinear reaction-diffusion models for bacterial biofilms