Published Paper

Inserted: 22 jul 2018
Last Updated: 22 jul 2018

Journal: CV PDE
Year: 2015
Doi: https://link.springer.com/article/10.1007/s00526-015-0926-y

Abstract:

In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates for gradients of solutions to the quasilinear parabolic equations: $u_t-div(A(x,t,\nabla u))=div(F),$ in a bounded domain $\Omega\times (0,T)\subset\mathbb{R}^{N+1}$, under minimal regularity assumptions on the boundary of domain and on nonlinearity $A$. Then results yields existence of a solution to the Riccati type parabolic equations: $u_t-div(A(x,t,\nabla u))=
\nabla u
^q+div(F)+\mu,$ where $q>1$ and $\mu$ is a bounded Radon measure.