Estimates for the deviation from exact solutions of variational problems with power growth functionals

Abstract

We study the nonlinear power growth variational problem J_{\alpha}[w]:=\int_{\Omega}\left[\frac{1}{\alpha}\left|\nabla w\right|^{\alpha}-fw\right]dx\rightarrow\textrm{min} and establish directly computable estimates for the deviation from exact solutions. In the case of superquadratic growth, these estimates are given in terms of the energy norm, in the subquadratic case we pass to estimates for the solution of the dual variational problem. Various boundary conditions are included in our considerations.