On the Regularity of Solutions to a Nonlinear Ultraparabolic Equation Arising in Mathematical Finance∗
نویسندگان
چکیده
We consider the following nonlinear degenerate parabolic equation which arises in some recent problems of mathematical finance: ∂xxu+ u∂yu− ∂tu = f. Using a harmonic analysis technique on Lie groups, we prove that, if the solution u satisfies condition ∂xu 6= 0 in an open set Ω ⊂ R and f ∈ C∞(Ω), then u ∈ C∞(Ω).
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