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- W3009409552 abstract "We consider nonlocal variational problems in $$L^p$$, like those that appear in peridynamics, where the functional object of the study is given by a double integral. It is known that convexity of the integrand implies the lower semicontinuity of the functional in the weak topology of $$L^p$$. If the integrand is not convex, a usual approach is to compute the relaxation, which is the lower semicontinuous envelope in the weak topology. In this paper we compute such a relaxation for a scalar problem with a double-well integrand. The relaxation is non-trivial, and, contrary to the local case, it cannot be represented as a double integral, as the original problem. Nonetheless, we show that, as for the local case, the relaxation can be expressed in terms of the energy of a suitable truncation of the considered function." @default.
- W3009409552 created "2020-03-13" @default.
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- W3009409552 date "2020-03-06" @default.
- W3009409552 modified "2023-09-30" @default.
- W3009409552 title "Relaxation of a scalar nonlocal variational problem with a double-well potential" @default.
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- W3009409552 doi "https://doi.org/10.1007/s00526-020-1728-4" @default.
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