Abstract
We consider second order degenerate parabolic equations with real, measurable, and time-dependent coefficients. We allow for degenerate ellipticity dictated by a spatial \(A_2\)-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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Open access funding provided by Uppsala University. K.N. was partially supported by grant 2022-03106 from the Swedish research council (VR).
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Ataei, A., Nyström, K. On Fundamental Solutions and Gaussian Bounds for Degenerate Parabolic Equations with Time-dependent Coefficients. Potential Anal (2024). https://doi.org/10.1007/s11118-024-10143-7
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DOI: https://doi.org/10.1007/s11118-024-10143-7