\(L^r\) estimates for degenerate elliptic problems
This paper deals with \(L^r\) estimates for degenerate elliptic problems, that is \[ -\text{div} \bigl(a(x,u,Du) \bigr)=f,\tag{1} \] with \(f\) in \(L^q\) for \(q\in [1,\infty)\), where the operator \(a(x,u,Du)\) satisfies \[ \alpha \bigl(|s|\bigr)|\xi|^p \leq\bigl(a (x,s,\xi), \xi\bigr) \quad \text{with }p>1. \tag{2} \] The author proves \(L^r\) estimates for the Dirichlet problem of (1) without symmetrization, which are sharp in some sense.
scientific article; zbMATH DE number 1785620