Calculus of Variations and Geometric Measure Theory

M. Carriero - A. Leaci - F. Tomarelli

Almansi decomposition and expansion of a polyharmonic function near a crack-tip

created by leaci on 07 Nov 2023
modified on 24 Mar 2024


Published Paper

Inserted: 7 nov 2023
Last Updated: 24 mar 2024

Journal: Journal of Convex Analysis
Volume: 31
Number: 2
Pages: 379-409
Year: 2024
Links: Journal of Convex Analysis


We study polyharmonic functions in 2-dimensional open sets with a flat crack: for these functions we show a decomposition of Almansi-type and make explicit the coefficients of a strongly converging expansion near the crack-tip.

Keywords: Crack-tip, crease-tip, Almansi decomposition , Image analysis, smooth cracks in elasticity, Power series expansion, biharmonic and polyharmonic functions , Free discontinuity problems, calculus of variations