Galerkin approximations in problems with \(p\)-Laplacian (Q2373995)

The Dirichlet problem \[ -\mathrm{div}(|\nabla u|^{p-2}\nabla u)= f,\,\,\, u|_{\partial \Omega}=0 \] is considered in a bounded smooth domain \(\Omega\subset R^d\), \(p>1\), \(X=W_0^{1,p}\) is the Sobolev space, \(u\in X\), \(f\) is a linear continuous functional on \(X\). A system of Galerkin approximations is constructed. Estimates of the difference between an exact and approximate solutions in the case of constant or variable exponent \(p\) are given.