The paper is concerned with the Enskog equation with a constant high density factor for large initial data in L^1(R^n). The initial boundary value problem is investigated for bounded domains with irregular boundaries. The proof of an H-theorem for the case of general domains and boundary conditions is given. The main result guarantees the existence of global solutions of boundary value problems for large initial data with all r'-moments initially finite and domains having boundary with finite Hausdorff measure and satisfying a cone condition.