Solutions of \(Lu = u^ \alpha\) dominated by \(L\)-harmonic functions

DOI10.1007/BF02790202zbMath0862.58047OpenAlexW2027268997MaRDI QIDQ1922211

E. B. Dynkin, S. E. Kuznetsov

Publication date: 25 May 1997

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02790202

zbMATH Keywords

elliptic equations\(L\)-harmonic functions

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Second-order elliptic equations (35J15) Elliptic equations on manifolds, general theory (58J05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Superprocesses and partial differential equations
• Singularités éliminables pour des équations semi-linéaires
• Construction and regularity of measure-valued Markov branching processes
• Boundary singularities of solutions of some nonlinear elliptic equations
• On regularity of superprocesses
• Removable boundary singularities for solutions of some nonlinear differential equations
• The Brownian snake and solutions of \(\Delta u = u^ 2\) in a domain
• Theory of capacities
• Minimal Excessive Measures and Functions
• An Introduction to Branching Measure-Valued Processes
• Superdiffusions and removable singularities for quasilinear partial differential equations
• THE SPACE OF EXITS OF A MARKOV PROCESS
• Stationary random distributions