On Dirichlets Boundary Value Problem : An Lp Theory Based on a Generalization of Gårdings Inequality Outline A priori estimates for solutions of linear elliptic functional equations with constant coefficients A representation for continuous linear functionals on W o m p (G) (1<p<) and its applications: A generalization of Gårdings inequality and existence theorems Regularity and existence theorems for uniformly elliptic functional equations.