Anisotropic classes of uniqueness of the solution of the Dirichlet problem for quasi-elliptic equations
Larisa Mikhailovna Kozhevnikova · Izvestiya Mathematics · 2006
We select a class of uniqueness of the solutions of the quasi-elliptic equation with the Dirichlet condition on the boundary of an unbounded domain and show that for domains with irregular behaviour of the boundary this class can be wider than that established in [10] for second-order elliptic equations. For the Laplace equation we construct an example of non-uniqueness of solution of the Dirichlet problem that shows that the class of uniqueness found in this paper cannot be essentially extended.