Solutions of nonlinear differential equations on a Riemannian manifold and their trace on the Martin boundary

DOI10.1090/S0002-9947-98-02006-6zbMath0911.60062OpenAlexW1485485216WikidataQ115284792 ScholiaQ115284792MaRDI QIDQ4211157

S. E. Kuznetsov, E. B. Dynkin

Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-02006-6

zbMATH Keywords

nonlinear differential equationsRiemannian manifoldsmoderate solutionssolution traces on Martin boundary

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Diffusion processes (60J60) Probabilistic potential theory (60J45) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (5)

Non-degenerate conditionings of the exit measures of super Brownian motion. ⋮ Boundary singularities of solutions of \(N\)-harmonic equations with absorption ⋮ Stochastic boundary values and boundary singularities for solutions of the equation \(Lu=u^\alpha\) ⋮ Isolated boundary singularities of semilinear elliptic equations ⋮ Unnamed Item

Cites Work

• Superprocesses and partial differential equations
• A probabilistic approach to one class of nonlinear differential equations
• The boundary trace of positive solutions of semilinear elliptic equations: The supercritical case
• Superdiffusion and parabolic nonlinear differential equations
• Solutions of \(Lu = u^ \alpha\) dominated by \(L\)-harmonic functions
• A probabilistic approach tо a nonlinear differential equation on a Riemannian manifold
• Trace on the boundary for solutions of nonlinear differential equations
• Superdiffusions and removable singularities for quasilinear partial differential equations
• Linear additive functionals of superdiffusions and related nonlinear P.D.E.
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