We give a regularity result for local minimizers \$u:Omega subset mathbb{R}^3 o mathbb{R}^3\$ 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 \$u^{alpha}\$ of \$u\$, we first prove a Caccioppoli's inequality and then apply De Giorgi's iteration method to get the boundedness of \$u^{alpha}\$. Our result can be applied to the polyconvex integral [int_Omega (sum_{alpha = 1}^{3} |D u^alpha|^{p} + |adj_2 Du|^q + |det Du|^{r}) dx] with suitable p,q,r &gt;1.

### Local Boundedness for Minimizers of Some Polyconvex Integrals

#### Abstract

We give a regularity result for local minimizers \$u:Omega subset mathbb{R}^3 o mathbb{R}^3\$ 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 \$u^{alpha}\$ of \$u\$, we first prove a Caccioppoli's inequality and then apply De Giorgi's iteration method to get the boundedness of \$u^{alpha}\$. Our result can be applied to the polyconvex integral [int_Omega (sum_{alpha = 1}^{3} |D u^alpha|^{p} + |adj_2 Du|^q + |det Du|^{r}) dx] with suitable p,q,r >1.
##### Scheda breve Scheda completa Scheda completa (DC)
2017
Cupini, Giovanni; Leonetti, Francesco; Mascolo, Elvira
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11585/579092`
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