We consider the Cauchy problem related to the partial differential equationLu ≡ Δ_x u + h(u)∂_y u − ∂_t u = f(·, u),where (x, y, t) ∈ R^N × R × ]0, T[, which arises in mathematical finance and in the theory of diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operatorof Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.

On the Cauchy problem for a non linear Kolmogorov equation / Pascucci, A.; Polidoro, Sergio. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 35,3:(2003), pp. 579-595.

On the Cauchy problem for a non linear Kolmogorov equation

POLIDORO, Sergio
2003

Abstract

We consider the Cauchy problem related to the partial differential equationLu ≡ Δ_x u + h(u)∂_y u − ∂_t u = f(·, u),where (x, y, t) ∈ R^N × R × ]0, T[, which arises in mathematical finance and in the theory of diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operatorof Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.
2003
35,3
579
595
On the Cauchy problem for a non linear Kolmogorov equation / Pascucci, A.; Polidoro, Sergio. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 35,3:(2003), pp. 579-595.
Pascucci, A.; Polidoro, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/421276
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