We give a regularity result for local minimizers u: Ω ⊂ R3→ R3 of a special class of polyconvex functionals. Under some structure assumptions on the energy density, we prove that local minimizers u are locally bounded. For each component uα of u, we first prove a Caccioppoli’s inequality and then apply De Giorgi’s iteration method to get the boundedness of uα. Our result can be applied to the polyconvex integral ∫Ω(∑α=13|Duα|p+|adj2Du|q+|detDu|r)dxwith suitable p, q, r> 1.
Local Boundedness for Minimizers of Some Polyconvex Integrals
LEONETTI, Francesco;
2017-01-01
Abstract
We give a regularity result for local minimizers u: Ω ⊂ R3→ R3 of a special class of polyconvex functionals. Under some structure assumptions on the energy density, we prove that local minimizers u are locally bounded. For each component uα of u, we first prove a Caccioppoli’s inequality and then apply De Giorgi’s iteration method to get the boundedness of uα. Our result can be applied to the polyconvex integral ∫Ω(∑α=13|Duα|p+|adj2Du|q+|detDu|r)dxwith suitable p, q, r> 1.File in questo prodotto:
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