| Abstract: | A jump relation for a boundary integral representation of solutions of hypoelliptic equations is described by a reflection principle. An orthogonal decomposition of L2 can be proved by the jump relation. In the orthogonal complement of the space of regular functions, i.e. the space of solutions of the homogeneous equation, the inhomogeneous adjoint equation has a solution with homogeneous boundary values. As a conclusion, one obtains Sobolev's regularity theorem. Furthermore it will be proved that the existence of the orthogonal decomposition and Sobolev's regularity theorem are equivalent. Theorems of Runge's type will be proved in order to determine countable dense subsets of the space of regular functions. |
