Differential and Integral Equations

Trace formulae of potentials for degenerate parabolic equations

Mukhtar Karazym and Durvudkhan Suragan

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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.

Article information

Source
Differential Integral Equations, Volume 33, Number 7/8 (2020), 337-360.

Dates
First available in Project Euclid: 14 July 2020

Permanent link to this document
https://projecteuclid.org/euclid.die/1594692053

Mathematical Reviews number (MathSciNet)
MR4122509

Subjects
Primary: 47G40: Potential operators [See also 31-XX] 35K65: Degenerate parabolic equations

Citation

Karazym, Mukhtar; Suragan, Durvudkhan. Trace formulae of potentials for degenerate parabolic equations. Differential Integral Equations 33 (2020), no. 7/8, 337--360. https://projecteuclid.org/euclid.die/1594692053


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