Let L0 be a degenerate second order elliptic operator with no zeroth order term in an m-dimensional domain G9 and let L = L0 + c. One divides the boundary of G into disjoint sets ∑1,∑2, ∑3,∑3the non characteristic part, and on ∑2 the "drift” is outward. When c is negative, the following Dirichlet problem has been considered in the literature: Lu =0 in G, u is prescribed on ∑2u ∑3. In the present work it is assume that c ≤ 0. Assuming additional boundary conditions on a certain finite number of points of ∑1, a unique solution of the Dirichlet problem is established.
ASJC Scopus subject areas
- Applied Mathematics