Quasilinear divergence form parabolic equations in Reifenberg flat domains (Q653903)

The authors consider a quasilinear prabolic equation in divergence form. They assume that the principal coefficients have a small BMO norm, and that the first order terms satisfy a controlled growth condition. They first prove the high integrability of the gradient and then they prove the existence of a weak solution. They assume that the domain satisfies a suitable Reifenberg condition (i.e., roughly speaking, that the domain is locally a topological disk). We recall that the condition of small BMO norm generalizes several results concerning coefficients of the principal part in VMO.