Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Removable Singularities of Harmonic Functions on Stratified Sets

Version 1 : Received: 22 February 2024 / Approved: 22 February 2024 / Online: 23 February 2024 (08:35:24 CET)

A peer-reviewed article of this Preprint also exists.

Dairbekov, N.S.; Penkin, O.M.; Savasteev, D.V. Removable Singularities of Harmonic Functions on Stratified Sets. Symmetry 2024, 16, 486. Dairbekov, N.S.; Penkin, O.M.; Savasteev, D.V. Removable Singularities of Harmonic Functions on Stratified Sets. Symmetry 2024, 16, 486.

Abstract

We prove an analog of the removable singularity theorem for bounded harmonic functions on stratified sets. The harmonic functions are understood in the sense of the soft Laplacian. The result can become one of the main technical components for extending the well-known Poincaré–Perron’s method of proving the solvability of the Dirichlet problem for the soft Laplacian.

Keywords

stratified measure; soft Laplacian; mean value; gradient flux

Subject

Computer Science and Mathematics, Mathematics

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