Some geometric features of the stable solutions of semilinear PDEs in the Heisenberg group are dealt with. A nonexistence result is given. The analysis is carried out by investigating the role of the right invariant vector fields: the monotonicity along these vector fields implies the stability of the solution and it naturally gives rise to geometrically interesting quantities.
Semilinear PDEs in the Heisenberg group: the role of the right invariant vector fields / I. Birindelli, F. Ferrari., E. Valdinoci. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 72:2(2010), pp. 987-997.
Semilinear PDEs in the Heisenberg group: the role of the right invariant vector fields
E. Valdinoci
2010
Abstract
Some geometric features of the stable solutions of semilinear PDEs in the Heisenberg group are dealt with. A nonexistence result is given. The analysis is carried out by investigating the role of the right invariant vector fields: the monotonicity along these vector fields implies the stability of the solution and it naturally gives rise to geometrically interesting quantities.
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