Localization principle and relaxation. (English) Zbl 1263.49011
Summary: Relaxation theorems for multiple integrals on \(W^{1,p}(\Omega;\mathbb R^N)\), where \(p\in ]1,\infty[\), are proved under general conditions on the integrand \(L:\mathbb M\to [0,\infty ]\) which is Borel measurable and not necessarily finite. We involve a localization principle that we previously used to prove a general lower semicontinuity result. We apply these general results to the relaxation of nonconvex integrals with exponential-growth.
MSC:
49J45 | Methods involving semicontinuity and convergence; relaxation |
49J10 | Existence theories for free problems in two or more independent variables |
74G65 | Energy minimization in equilibrium problems in solid mechanics |