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arXiv · 2509.09519

$H^\infty$-calculus for the Dirichlet Laplacian on conical domains

Petru A. Cioica-Licht·Emiel Lorist·P. Tobias Werner
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Abstract

We establish boundedness of the $H^\infty$-calculus for the Dirichlet Laplacian on conical domains in $\mathbb{R}^d$ and corresponding wedges on $L^p$-spaces with mixed weights. The weights are based on both the distance to the boundary and the distance to the tip/edge of the cone/wedge. Our main motivation comes from the study of stochastic partial differential equations and associated degenerate deterministic parabolic equations on non-smooth domains. As a consequence of our analysis, we also obtain maximal $L^p$-regularity for the Poisson equation on conical domains in appropriate weighted Sobolev spaces.

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Petru A. Cioica-Licht, Emiel Lorist, P. Tobias Werner. 2025-09-11. $H^\infty$-calculus for the Dirichlet Laplacian on conical domains. https://arxiv.org/abs/2509.09519

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