Summability and existence results for quasilinear parabolic equations with Hardy potential term
The authors study the equation \[ u_t = \text{div} (a(x,t,u, \nabla u)) = \lambda \frac{u}{|x|^2} + f, \] where \(a\) is a Caratheodory function and \(f\) is in \(L^r(L^q)\) with \(r,q \geq 1\). The authors prove the existence and the summability of the solutions. Moreover they analyze in detail how the presence of this singular potential and the summability of the datum \(f\) influence the regularity of the solutions.
scientific article; zbMATH DE number 6138206
scientific article