Some refinements of the Hodge decomposition and applications (Q5938882)

The authors deal with the Hodge decomposition due to the well-known result of Iwaniec. They extend the nonlinear Hodge decomposition to other vector fields and give applications to Leray-Lions type equations with very weak assumptions on data. The new types of Hodge decomposition obtained by the authors allow them that to say that solving the equation NEWLINE\[NEWLINE-\text{div}(\widehat a(x,u,Du))+ F(x,u,Du)= \muNEWLINE\]NEWLINE in \(V_0\), \(W_0\), or \(L^{1,n}_0(\Omega)\) is totally equivalent, if \(\widehat a\) and \(F\) satisfy some natural conditions. Here \(V_0\), \(W_0\), \(L^{1,n}_0\) are physically relevant functional spaces.