Abstract
We consider the Cauchy problem related to the partial differential equation Lu ≡ ∆xu + h(u)∂yu − ∂tu = 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 operator of Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.
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