Degenerate elliptic equations and nonuniqueness of solutions to the Kolmogorov equation

DOI10.1134/S1064562419040112zbMath1433.35018OpenAlexW4252816834WikidataQ127200080 ScholiaQ127200080MaRDI QIDQ2279771

T. I. Krasovitskii

Publication date: 13 December 2019

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562419040112

zbMATH Keywords

Kolmogorov equationnonuniqueness of probability solutions

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (7)

Uniqueness of a probability solution to the Kolmogorov equation with a diffusion matrix satisfying Dini's condition ⋮ Zvonkin’s transform and the regularity of solutions to double divergence form elliptic equations ⋮ Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes ⋮ Superposition principle for the Fokker-Planck-Kolmogorov equations with unbounded coefficients ⋮ The Kolmogorov problem on uniqueness of probability solutions of a parabolic equation ⋮ On nonuniqueness of probability solutions to the Cauchy problem for the Fokker-Planck-Kolmogorov equation ⋮ On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation

Cites Work

• On nonuniqueness of solutions to elliptic equations for probability measures
• Criteria for well-posedness of degenerate elliptic and parabolic problems
• Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung
• On non-uniqueness of probability solutions to the two-dimensional stationary Fokker-Planck-Kolmogorov equation
• Stability of regime-switching stochastic differential equations
• Remarks on the uniqueness of a solution of the Dirichlet problem for second-order elliptic equations with lower-order terms
• Fokker–Planck–Kolmogorov Equations
• Uniqueness of solutions of elliptic equations and uniqueness of invariant measures of diffusions
• Dirichlet Problem for Degenerate Elliptic Equations
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