Calculus of Variations and Geometric Measure Theory

Q. H. Nguyen

Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data

created by nguyen on 22 Jul 2018


Published Paper

Inserted: 22 jul 2018
Last Updated: 22 jul 2018

Journal: CV PDE
Year: 2015


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.