We prove three density theorems, in the strong BD topology, for the three subspaces of SBD functions: SBD; SBDp∞, where the absolutely continuous part of the symmetric gradient is in Lp, with p > 1; SBDp, whose functions are in SBDp∞ and the jump set has finite Hn-1-measure. We compare them with existing results, discussing related approximation of fracture energies.
Density in SBD and approximation of fracture energies / Crismale, V.. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 30:3(2019), pp. 533-542. [10.4171/RLM/859]
Density in SBD and approximation of fracture energies
Crismale V.
2019
Abstract
We prove three density theorems, in the strong BD topology, for the three subspaces of SBD functions: SBD; SBDp∞, where the absolutely continuous part of the symmetric gradient is in Lp, with p > 1; SBDp, whose functions are in SBDp∞ and the jump set has finite Hn-1-measure. We compare them with existing results, discussing related approximation of fracture energies.File allegati a questo prodotto
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