*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.