This paper is concerned with regularity of minimizers of integral functionals with polyconvex potentials. In particular we obtain bounds on the difference $|u-u_*|_infty$ for minimizers $u:Omega subset mathbb{R}^3 o mathbb{R}^3$ of problem % egin{equation*} minleft{ int_Omega f(x,Dv(x))dx,quad vin u_* + W_0^{1,p}(Omega,R^3) ight}. end{equation*}
An estimate concerning the difference between minimizer and boundary value in some polyconvex problems
Giulia Treu
2022
Abstract
This paper is concerned with regularity of minimizers of integral functionals with polyconvex potentials. In particular we obtain bounds on the difference $|u-u_*|_infty$ for minimizers $u:Omega subset mathbb{R}^3 o mathbb{R}^3$ of problem % egin{equation*} minleft{ int_Omega f(x,Dv(x))dx,quad vin u_* + W_0^{1,p}(Omega,R^3) ight}. end{equation*}
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