Trace formulae of potentials for degenerate parabolic equations
Mukhtar Karazym, Durvudkhan Suragan
TL;DR
This paper investigates the properties of potentials and Poisson integrals for multi-dimensional degenerate parabolic equations, deriving trace formulae that address Kac's problem in cylindrical domains.
Contribution
It introduces new trace formulae for heat volume potentials and Poisson integrals specific to degenerate parabolic equations, solving a longstanding problem in this area.
Findings
Derived trace formulae for degenerate parabolic equations
Solved Kac's problem for cylindrical domains
Analyzed properties of volume and layer potentials
Abstract
In this paper, we analyze main properties of the volume and layer potentials as well as the Poisson integral for a multi-dimensional degenerate parabolic equation. As consequences, we obtain trace formulae of the heat volume potential and the Poisson integral which solve Kac's problem for degenerate parabolic equations in cylindrical domains.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Nonlinear Partial Differential Equations · Differential Equations and Numerical Methods