Abstract

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.

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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

Mathematics Subject Classification

31A30; 49J45, 35J40

Suggested citation

M. Carriero, A. Leaci, F. Tomarelli. “Almansi Decomposition and Expansion of a Polyharmonic Function Near a Crack-Tip.” Journal of Convex Analysis 31 (2024), No. 2, 379–409. https://doi.org/10.68381/jca31024

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press.