Nonsolvability of the asymptotic Dirichlet problems for some quasilinear elliptic PDEs on Hadamard manifolds

摘要

We show, by modifying Borb\'ely's example, that there are $3$-dimen\-sionalCartan-Hadamard manifolds $M$, with sectional curvatures $\le -1$, such thatthe asymptotic Dirichlet problem for a class of quasilinear elliptic PDEs,including the minimal graph equation, is not solvable.