We consider the Cauchy problem related to the partial differential equation Lu = Δxu + h(u)∂yu - ∂ tu = f(·, u), where (x,y,t) ∈ ℝN × ℝ ×]0,T[, which arises in mathematical finance and in the theory oi diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operator of Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.
On the cauchy problem for a nonlinear Kolmogorov equation
PASCUCCI, ANDREA;
2004
Abstract
We consider the Cauchy problem related to the partial differential equation Lu = Δxu + h(u)∂yu - ∂ tu = f(·, u), where (x,y,t) ∈ ℝN × ℝ ×]0,T[, which arises in mathematical finance and in the theory oi diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operator of Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.File in questo prodotto:
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