Stochastic boundary values and boundary singularities for solutions of the equation \(Lu=u^\alpha\)

DOI10.1006/jfan.1997.3176zbMath0903.60068OpenAlexW1984668510MaRDI QIDQ1381582

E. B. Dynkin

Publication date: 5 January 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1997.3176

zbMATH Keywords

Markov process\(L\)-diffusion

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation
• Superprocesses and partial differential equations
• A probabilistic approach to one class of nonlinear differential equations
• Superdiffusion and parabolic nonlinear differential equations
• Natural linear additive functionals of superprocesses
• Nonlinear parabolic P.D.E. and additive functionals of superdiffusions
• The Brownian snake and solutions of \(\Delta u = u^ 2\) in a domain
• Solutions of \(Lu = u^ \alpha\) dominated by \(L\)-harmonic functions
• Theory of capacities
• Solutions of nonlinear differential equations on a Riemannian manifold and their trace on the Martin boundary
• An Introduction to Branching Measure-Valued Processes
• A probabilistic Poisson representation for positive solutions of ?u = u2 in a planar domain
• A new relation between diffusions and superdiffusions with applications to the equation lu=u
• Superdiffusions and removable singularities for quasilinear partial differential equations