Backward Ornstein-Uhlenbeck Transition Operators and Mild Solutions of Non-Autonomous Hamilton-Jacobi Equations in Banach Spaces Academic Article

journal

  • Journal Of Mathematics Research

abstract

  • In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily extended to non-autonomous Hamilton-Jacobi equations in Banach spaces. The main tool is the regularizing property of Ornstein-Uhlenbeck transition evolution operators for stochastic Cauchy problems in Banach spaces with time-dependent coefficients.

publication date

  • 2014-1-1

edition

  • 6

keywords

  • Banach space
  • Cauchy Problem
  • Coefficient
  • Evolution Operator
  • Hamilton-Jacobi
  • Hamilton-Jacobi Equation
  • Hilbert space
  • Infinite-dimensional Spaces
  • Mild Solution
  • Nonautonomous Equation
  • Ornstein-Uhlenbeck Operator
  • Semilinear
  • Transition Operator

International Standard Serial Number (ISSN)

  • 1916-9795

number of pages

  • 21

start page

  • 55

end page

  • 76