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

摘要

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