The Cauchy-Dirichlet Problem for a Class of Linear Parabolic Differential Equations with Unbounded Coefficients in an Unbounded Domain. (22nd June 2011) - Rubio, Gerardo
Abstract : We consider the Cauchy-Dirichlet problem in[ 0, ∞ ) × D for a class of linear parabolic partial differential equations. We assume thatD ⊂ ℝ d 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.