On Fundamental Solutions and Gaussian Bounds for Degenerate Parabolic Equations with Time-dependent Coefficients

Alireza Ataei, Kaj Nyström

Type: Article

Publication Date: 2024-05-06

Citations: 0

DOI: https://doi.org/10.1007/s11118-024-10143-7

Abstract

Abstract We consider second order degenerate parabolic equations with real, measurable, and time-dependent coefficients. We allow for degenerate ellipticity dictated by a spatial $$A_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -weight. We prove the existence of a fundamental solution and derive Gaussian bounds. Our construction is based on the original work of Kato (Nagoya Math. J. 19 , 93–125 1961).

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+ PDF Chat	On the behavior of the solutions of degenerate parabolic equations	1999	Kazuhiro Ishige
+ PDF Chat	Abstract Evolution Equations of Parabolic Type in Banach and Hilbert Spaces	1961	Tosio Kato
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+ PDF Chat	Bounds for the fundamental solution of a parabolic equation	1967	D. G. Aronson
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+	A new proof of Moser's parabolic harnack inequality using the old ideas of Nash	1986	Eugene B. Fabes D. W. Stroock
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