L&lt;sup&gt;p&lt;/sup&gt;-estimates for the square root of elliptic systems with mixed boundary conditions II

Bechtel, S.

doi:10.1016/j.jde.2023.09.036

L^p-estimates for the square root of elliptic systems with mixed boundary conditions II

Title

L^p-estimates for the square root of elliptic systems with mixed boundary conditions II

Author

Bechtel, S. (TU Delft Analysis)

Date

2024

Abstract

We show L^p-estimates for square roots of second order complex elliptic systems L in divergence form on open sets in R^d subject to mixed boundary conditions. The underlying set is supposed to be locally uniform near the Neumann boundary part, and the Dirichlet boundary part is Ahlfors–David regular. The lower endpoint for the interval where such estimates are available is characterized by p-boundedness properties of the semigroup generated by −L, and the upper endpoint by extrapolation properties of the Lax–Milgram isomorphism. Also, we show that the extrapolation range is relatively open in (1,∞).

Subject

Calderón–Zygmund decomposition for Sobolev functions
Complex elliptic systems of second order
Hardy's inequality
Kato square root problem
Lax–Milgram isomorphism
Mixed boundary conditions

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http://resolver.tudelft.nl/uuid:67246fb8-d0c7-4dde-b931-541656d0e860

DOI

https://doi.org/10.1016/j.jde.2023.09.036

ISSN

0022-0396

Source

Journal of Differential Equations, 379, 104-124

Part of collection

Institutional Repository