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; Polidoro, Sergio. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 35:3(2004), pp. 579-595. [10.1137/S0036141001399349]

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.
2004
On the cauchy problem for a nonlinear Kolmogorov equation / Pascucci, Andrea; Polidoro, Sergio. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 35:3(2004), pp. 579-595. [10.1137/S0036141001399349]
Pascucci, Andrea; Polidoro, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/594984
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