\(C^ k\)-regularity for the \({\bar \partial}\)-equation on strictly pseudoconvex domains with piecewise smooth boundaries
The authors study the equation \({\bar \partial}u=f\) on a piecewise strictly pseudoconvex domain in \({\mathbb{C}}^ n\). A linear solution operator \(T^*_ q\) was given, such that, if f is a \({\bar\partial}\)-closed q-form, which is \({\mathcal C}^ k\)-regular up to the boundary, \(T^*_ qf=u\) satisfies the following \({\mathcal C}^ k\)-estimates: \[ \| u\|_{{\mathcal C}^{k-\epsilon}}\leq const(k,\epsilon)\cdot \| f\|_{{\mathcal C}^ k} \] for arbitrary real numbers \(0<\epsilon\).
scientific article; zbMATH DE number 4101587