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Research Paper | Synapse

March 14, 2026

Green Function of the Zaremba Problem for the Heat Operator

Key Points

To prove the existence and uniqueness of the Green’s function for heat operator under specific boundary conditions.
Considered a parabolic initial-boundary value problem
Applied homogeneous Zaremba boundary conditions
Focused on a cylinder with a Lipschitz bounded base domain
Demonstrated the existence of the Green’s function
Established uniqueness for the Green’s function under the specified conditions

Abstract

A parabolic initial-boundary value problem with homogeneous Zaremba boundary conditions in a cylinder whose base is a strictly Lipschitz bounded domain is considered, for which a theorem of the existence and uniqueness of the Green’s function is proved.

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Cite this study

A. G Chechkina (Wed,) studied this question.

synapsesocial.com/papers/69b4adc718185d8a39801b56 — DOI: https://doi.org/10.7868/s3034504925060077

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A. G Chechkina

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