Local Regularity for Minimizers of Obstacle Problems of Some Anisotropic Integral Functionals
Hongya Gao, Gao Yanmin, Guo Kaili, Miaomiao Jia · Mathematica Eterna · 2015
A local regularity result is obtained for minimizers u ∈ Kψ = n u ∈ W 1,(qi) loc (â¦) : u ≥ ψ}, qi > 1, ∀i = 1, · · · , N, of anisotropic integral functionals of the type F(u; â¦) = Z ⦠f(x, u, Du)dx, where the Carath´eodory function f(x, u, Du) = f0(x, u, Du)+f1(x, u, Du), f0(x, s, z) grows like PN i=1 |zi | qi , and f1(x, s, z) satisfies some controllable growth condition.