Journal of Convex Analysis 31 (2024), No. 2, 379--409
Copyright Heldermann Verlag 2024
Almansi Decomposition and Expansion of a Polyharmonic Function Near a Crack-Tip
Michele Carriero
Dip. di Matematica e Fisica "Ennio De Giorgi", Università del Salento, Lecce, Italy
michele.carriero@unisalento.it
Antonio Leaci
Dip. di Matematica e Fisica "Ennio De Giorgi", Università del Salento, Lecce, Italy
antonio.leaci@unisalento.it
Franco Tomarelli
Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
franco.tomarelli@polimi.it
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, power series expansion, biharmonic functions, polyharmonic functions, image analysis, smooth cracks in elasticity, free discontinuity, calculus of variations.
MSC: 31A30; 49J45, 35J40.
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