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[en] 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 Ω subset of Rn+1 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
Journal
Izvestiya. Mathematics; ISSN 1064-5632; 
; v. 70(6); p. 1165-1200
; v. 70(6); p. 1165-1200