The Cauchy-Dirichlet Problem for a Class of Linear Parabolic Differential Equations with Unbounded Coefficients in an Unbounded Domain

الملخص EN

We consider the Cauchy-Dirichlet problem in [0,∞)×D for a class of linear parabolic partial differential equations.

We assume that D⊂ℝd is an unbounded, open, connected set with regular boundary.

Our hypotheses are unbounded and locally Lipschitz coefficients, not necessarily differentiable, with continuous data and local uniform ellipticity.

We construct a classical solution to the nonhomogeneous Cauchy-Dirichlet problem using stochastic differential equations and parabolic differential equations in bounded domains.