Abstract
We consider the following nonlinear degenerate parabolic equation which arises in some recent problems of mathematical finance: $$ \partial_{xx} u + u \partial_{y} u - \partial_{t} u =f. $$ Using a harmonic analysis technique on Lie groups, we prove that, if the solution $u$ satisfies condition $\partial_x u \neq 0$ in an open set $\Omega \subset \mathbb R^3$ and $f \in C^{\infty}(\Omega)$, then $u \in C^{\infty}(\Omega)$.
Citation
Giovanna Citti. Andrea Pascucci. Sergio Polidoro. "On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance." Differential Integral Equations 14 (6) 701 - 738, 2001. https://doi.org/10.57262/die/1356123243
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