On fundamental solutions and Gaussian bounds for degenerate parabolic equations with time-dependent coefficients

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 \cite{Kato}.

arXiv commentIn this version, we have added more details in Section 3 of the paper. Section 3 contains the proof of the uniqueness part of our main result and as the argument uses Steklov averages and contains some subtleties, we now supply the full detail