On \(\mathrm{Lip}^m\)-reflection of harmonic functions over boundaries of simple Carathéodory domains

DOI10.1007/s13324-019-00296-9zbMath1430.31003OpenAlexW2940731814MaRDI QIDQ2009431

Konstantin Yu. Fedorovskiy, Peter V. Paramonov

Publication date: 28 November 2019

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13324-019-00296-9

zbMATH Keywords

harmonic measurePoisson operatorharmonic reflection operatorLipschitz-Hölder spacessimple Carathéodory domain

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary behavior of harmonic functions in higher dimensions (31B25)

Related Items (3)

On \(\mathrm{Lip}( \omega )\)-continuity of the operator of harmonic reflection over boundaries of simple Carathéodory domains ⋮ On -reflection of harmonic functions and -approximation by harmonic polynomials ⋮ Heating long pipes

Cites Work

• Unnamed Item
• Unnamed Item
• The boundary modulus of continuity of harmonic functions
• Smooth potentials with prescribed boundary behaviour
• Extremal barriers on cones with Phragmén-Lindelöf theorems and other applications
• $ C^1$-approximation and extension of subharmonic functions
• $ C^1$-extension and $ C^1$-reflection of subharmonic functions from Lyapunov-Dini domains into $ \mathbb R^N$
• The Integrability of Superharmonic Functions on Lipschitz Domains
• Subharmonic Extensions and Approximations
• $ C^m$-extension of subharmonic functions

This page was built for publication: On \(\mathrm{Lip}^m\)-reflection of harmonic functions over boundaries of simple Carathéodory domains