Quasiminimizers in one dimension: integrability of the derivate, inverse function and obstacle problems (Q2460778)

The paper deals with the properties of a \(K\)-quasiminimizer \(u\) for the one-dimensional \(p\)-Dirichlet integral. By using the higher integrability results of weights in the Gehring class, the authors prove that \(u\) is also a \(K^{\prime}\)-quasiminimizer for \(q\)-Dirichlet integral, with \(1\leq q \leq p_1(p,K)\) and the exact value of \(p_1(p,K)\) is given. Morever it is showed that the inverse fuction of a \((p,K)\)-quasiminimizers is a quasiminimizer for the \(s\)-Dirichlet integral, with a specified range on \(s\).