On the regularity of solutions to the plastoelasticity problem
Arrigo Cellina · Advances in Calculus of Variations · 2017
Abstract We prove the local regularity of solutions to the problem of minimizing ∫ Ω [ L ∞ ( ∇ v ( x ) ) + f ( x ) v ( x ) ] 𝑑 x on u 0 + W 0 1 , ∞ ( Ω ) , \int_{\Omega}\bigl{[}L_{\infty}( abla v(x))+f(x)v(x)\bigr{]}\,dx\quad\text{on% }u^{0}+W^{1,\infty}_{0}(\Omega), where L ∞ {L_{\infty}} is either 1 2 | ξ | 2 {\frac{1}{2}\lvert\xi\rvert^{2}} for | ξ | ≤ 1 {\lvert\xi\rvert\leq 1} and + ∞ {+\infty} for | ξ | > 1 {\lvert\xi\rvert>1} , or a more general convex, extended-valued function.