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By Baisheng (-mis) Zhou


L p-mean coercivity, regularity and relaxation in the calculus of variations. Nonlinear Anal. 46 (2001), no. 6, Ser. A: Theory Methods, 835–851. The paper deals with the minimization of a multiple integral of the type Ip(u, D) = D [f(∇u(x))]p dx, where the linear growth condition on f is replaced by a weaker one called L p-mean coercivity. Moreover, it is supposed that f ≥ 0 and the set {f = 0} is nonempty. One of the main results asserts that the zero set of the quasiconvexification of f p equals the zero set of the quasiconvexification of f p+ε for some ε> 0. Further, a version of Ekeland’s variational principle is proved, as well as higher regularity results for the first order Hamilton-Jacobi system. Reviewed by Martin Kruˇzí

Year: 2013
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