Fundamental solutions for degenerate parabolic equations: existence, properties, and some applications

DOI10.1007/s10958-023-06810-6OpenAlexW4389953964MaRDI QIDQ6147686

I. P. Medynskyj

Publication date: 1 February 2024

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-023-06810-6

zbMATH Keywords

parabolic equationsvolume potentialintegral representations of solutionsfundamental solution of Cauchy problemdegeneration on initial hyperplaneultraparabolic Kolmogorov-type equations

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Degenerate parabolic equations (35K65) Integral representations of solutions to PDEs (35C15) Initial value problems for second-order parabolic equations (35K15) Ultraparabolic equations, pseudoparabolic equations, etc. (35K70)

Cites Work

• Solutions of parabolic equations from families of Banach spaces depending on time
• Parabolic boundary value problems
• Zufällige Bewegungen. (Zur Theorie der Brownschen Bewegung.)
• On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance
• Analytic methods in the theory of differential and pseudo-differential equations of parabolic type
• A continuous dependence result for ultraparabolic equations in option pricing
• On applications of the Levi method in the theory of parabolic equations
• Two-sided estimates of fundamental solutions of second-order parabolic equations, and some applications
• LINEAR EQUATIONS OF THE SECOND ORDER OF PARABOLIC TYPE
• On the Classical Fundamental Solutions of the Cauchy Problem for Ultraparabolic Kolmogorov-Type Equations with Two Groups of Spatial Variables
• Properties of integrals which have the type of derivatives of volume potentials for one ultraparabolic arbitrary order equation
• ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Fundamental solutions for degenerate parabolic equations: existence, properties, and some applications