A new inequality for superdiffusions and its applications to nonlinear differential equations

DOI10.1090/S1079-6762-04-00131-3zbMath1080.60066OpenAlexW1435186560MaRDI QIDQ4681007

E. B. Dynkin

Publication date: 14 June 2005

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/226319

zbMATH Keywords

positive solutionstochastic equationsemi-linear elliptic equation\(\sigma\)-moderate solution

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (10)

Bessel capacities on compact manifolds and their relation to Poisson capacities ⋮ Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations ⋮ Boundary value problems with measures for elliptic equations with singular potentials ⋮ Positive solutions of a class of semilinear equations with absorption and Schrödinger equations ⋮ A class of boundary traces for solutions of the equation \(Lu=\psi (u)\) ⋮ Moderate solutions of semilinear elliptic equations with Hardy potential ⋮ Capacitary estimates of positive solutions of semilinear elliptic equations with absorption ⋮ An elliptic semilinear equation with source term and boundary measure data: the supercritical case ⋮ Maximal solutions for \(-\Delta u+u^q=0\) in open and finely open sets ⋮ Semilinear elliptic equations with subcritical absorption in Lipschitz domains

Cites Work

• Unnamed Item
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• A probabilistic approach to one class of nonlinear differential equations
• Poisson capacities
• Capacitary estimates of positive solutions of semilinear elliptic equations with absorption
• On upper bounds for positive solutions of semilinear equations
• Absolute continuity results for superdiffusions with applications to differential equations
• Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation
• An upper bound for positive solutions of the equation Δ𝑢=𝑢^{𝛼}

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