TY - JOUR
T1 - Rigidity results in diffusion Markov triples
AU - Dipierro, S.
AU - Pinamonti, A.
AU - Valdinoci, E.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - We consider stable solutions of semilinear equations in a very general setting. The equation is set on a Polish topological space endowed with a measure and the linear operator is induced by a carré du champs (equivalently, the equation is set in a diffusion Markov triple). Under suitable curvature dimension conditions, we establish that stable solutions with integrable carré du champs are necessarily constant (weaker conditions characterize the structure of the carré du champs and carré du champ itéré). The proofs are based on a geometric Poincaré formula in this setting. From the general theorems established, several previous results are obtained as particular cases and new ones are provided as well.
AB - We consider stable solutions of semilinear equations in a very general setting. The equation is set on a Polish topological space endowed with a measure and the linear operator is induced by a carré du champs (equivalently, the equation is set in a diffusion Markov triple). Under suitable curvature dimension conditions, we establish that stable solutions with integrable carré du champs are necessarily constant (weaker conditions characterize the structure of the carré du champs and carré du champ itéré). The proofs are based on a geometric Poincaré formula in this setting. From the general theorems established, several previous results are obtained as particular cases and new ones are provided as well.
UR - http://www.scopus.com/inward/record.url?scp=85048710910&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2018.06.005
DO - 10.1016/j.jfa.2018.06.005
M3 - Article
SN - 0022-1236
VL - 276
SP - 785
EP - 814
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 3
ER -