Maximal regularity for elliptic operators with second-order discontinuous coefficients
The authors consider the maximal regularity for parabolic problems associated to the second-order elliptic operator \[ L=\Delta +(a-1)\sum_{i,j=1}^N \frac{x_ix_j}{|x|^2}D_{ij}+\frac{c}{|x|^2}.\nabla -b |x|^{-1} \] with \(a>0\) and \(b,c\in \mathbb R.\) It is proved that the assocated parabolic problem \[ u_t(t)-Lu(t)=f(t)\quad t>0,\qquad u(0)=0 \] has maximal \(L^q\) regularity, that is for each \(f\in L^q(0,\infty;X)\) there exists a solution \(u\in W^{1,q}(0,\infty; X) \cap L^q(0,\infty; D(L)) \) where \(D(L)\) is the domain of \(L\) in \(X\).
scientific article; zbMATH DE number 7451417
scientific article