Resolutions of parabolic equations in non-symmetric conical domains

This article is devoted to the analysis of a two-space dimensional linear parabolic equation, subject to Cauchy-Dirichlet boundary conditions. The problem is set in a conical type domain and the right hand side term of the equation is taken in a Lebesgue space. One of the main issues of this work is that the domain can possibly be non regular. This work is an extension of the symmetric case studied in Sadallah [13].