Browsing by Author "Savasteev D.V."

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    HARNACK’S INEQUALITY FOR HARMONIC FUNCTIONS ON STRATIFIED SETS
    (Siberian Mathematical Journal, 2023) Dairbekov N.S.; Penkin O.M.; Savasteev D.V.
    We prove Harnack’s inequality for nonnegative harmonic functions in the sense of the “soft” Laplacian on a stratified set with flat strata.
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    Removable Singularities of Harmonic Functions on Stratified Sets
    (MDPI, 2024) Dairbekov N.S.; Penkin O.M.; Savasteev D.V.
    There are deep historical connections between symmetry, harmonic functions, and stratified sets. In this article, 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.