Hölder regularity for a Kolmogorov equation
Andrea Pascucci · Transactions of the American Mathematical Society · 2002
We study the interior regularity properties of the solutions to the degenerate parabolic equation, \[ Δ x u + b ∂ y u − ∂ t u = f , ( x , y , t ) ∈ R N × R × R , \Delta _{x}u+b\partial _{y}u-\partial _{t}u=f, \qquad (x,y,t)\in \mathbb {R}^{N}\times \mathbb {R}\times \mathbb {R}, \] which arises in mathematical finance and in the theory of diffusion processes.