Rigidity results in diffusion Markov triples
Copyright policy )Rigidity results in diffusion Markov triples
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.
Mathematics - Analysis of PDEs, Diffusion processes and stochastic analysis on manifolds, Stable solutions; Bakry-Emery-Gentil-Ledoux; Gamma-calculus; Rigidity results; Stratified groups, Bakry-Emery-Gentil-Ledoux gamma-calculus, rigidity results, FOS: Mathematics, Initial value problems for linear higher-order PDEs, Stable solutionsBakry–Emery–Gentil–Ledoux Gamma-calculusRigidity resultsStratified groups, stratified groups, stable solutions, Analysis of PDEs (math.AP)
Mathematics - Analysis of PDEs, Diffusion processes and stochastic analysis on manifolds, Stable solutions; Bakry-Emery-Gentil-Ledoux; Gamma-calculus; Rigidity results; Stratified groups, Bakry-Emery-Gentil-Ledoux gamma-calculus, rigidity results, FOS: Mathematics, Initial value problems for linear higher-order PDEs, Stable solutionsBakry–Emery–Gentil–Ledoux Gamma-calculusRigidity resultsStratified groups, stratified groups, stable solutions, Analysis of PDEs (math.AP)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!