We study the existence of Lipschitz minimizers of integral functionals with polyconvex and nonpolyconvex energy density, which depends on the space variable. The attainment results are obtained passing by the minimization of an auxiliary functional and the study of existence of solutions for the prescribed Jacobian equation. Moreover some special classes of nonpolyconvex functionals and the radial case are studied. These functionals are worthy of interest, because of their applications in physics, mainly in elasticity theory and in the problem of the equilibrium of gases.
Existence of minimizers for polyconvex and nonpolyconvex problems / G.Cupini; E. Mascolo. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 44:(2005), pp. 1370-1390. [10.1137/040611999]
Existence of minimizers for polyconvex and nonpolyconvex problems
MASCOLO, ELVIRA
2005
Abstract
We study the existence of Lipschitz minimizers of integral functionals with polyconvex and nonpolyconvex energy density, which depends on the space variable. The attainment results are obtained passing by the minimization of an auxiliary functional and the study of existence of solutions for the prescribed Jacobian equation. Moreover some special classes of nonpolyconvex functionals and the radial case are studied. These functionals are worthy of interest, because of their applications in physics, mainly in elasticity theory and in the problem of the equilibrium of gases.File | Dimensione | Formato | |
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