On Fundamental Solutions and Gaussian Bounds for Degenerate Parabolic Equations with Time-dependent Coefficients
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 $$A_2$$ <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 …