An Inhomogeneous Dirichlet Problem For A Non-Hypoelliptic Linear Partial Differential Operator

Abstract

. In this paper we state an inhomogeneous Dirichlet problem for a class of linear partial differential operators which are non-hypoelliptic. We prove uniqueness, existence and regularity results for its solutions. 1. Introduction In [1] K. Doppel and the present author stated a homogeneous Dirichlet problem for non-hypoelliptic linear partial differential operators, especially for a product of uniformly elliptic differential operators with smooth coefficient functions. Here we state an inhomogeneous Dirichlet problem for the same class of partial differential operators. The related homogeneous problem turns out to be an equivalent reformulation of the homogeneous Dirichlet problem in [1]. But this new formulation yields more general results than the former one. For further details of this problem and for some literature relevant in this context we refer to the introduction in [1]. 2. The inhomogeneous problem Most of the definitions used here are taken from [1]. We recapitulate onl..

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