Abstract
We derive directly computable estimates of differences between approximate solutions and minimizers of the variational problem $$J_\alpha \left[ w \right]: = \int\limits_\Omega {\left[ {\frac{1}{\alpha }\left| {\nabla w} \right|^\alpha - fw} \right]dx} \to \min .$$ . If the functional has a superquadratic growth, then the estimate is given in terms of the natural energy norm. For problems with subquadratic growth, it is more convenient to derive such estimates in terms of the dual variational problem. The estimates are obtained for Dirichlet, Neumann, and mixed boundary conditions. Bibliography: 22 titles.
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