Parabolic differential equations with Hölder continuous and unbounded coefficients
Thomas Deck, Susanne Kruse · MADOC (University of Mannheim) · 2000
We consider one-dimensional linear parabolic differential equations with Hölder continuous, unbounded drifts. We first extend the classical parametrix method of E. Levi to prove existence of fundamental solutions. From this we derive existence and uniqueness of solutions for the corresponding Cauchy problem. Our results extend to equations in higher dimensions with additional unbounded potential.