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The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent

  • Guy Bouchitté (a1), Irene Fonseca (a2) and Jan Malý (a3)

Abstract

The characterisation of the bulk energy density of the relaxation in W1, P(Ω; ℝd) of a functional

is obtained for p > qq/N, where uW1, P(Ω; ℝd), and f is a continuous function on the set of d × N matrices verifying

for some constant C > 0 and 1 ≦ q < + ∞. Typical examples may be found in cavitation and related theories. Standard techniques cannot be used due to the gap between the exponent q of the growth condition and the exponent p of the integrability of the macroscopic strain ∇u. A recently introduced global method for relaxation and fine Sobolev trace and extension theorems are applied.

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The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent

  • Guy Bouchitté (a1), Irene Fonseca (a2) and Jan Malý (a3)

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