Maximum principle for non-uniformly parabolic equations and applications

Abstract

In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi's iteration. As applications, we show the existence of weak solutions for possibly degenerate stochastic differential equations with singular diffusion and drift coefficients. Moreover, by the Markov selection theorem of Krylov [8], we also establish the existence of the associated strong Markov family.

30pages

References in corpus (2)

• Stochastic Lagrangian path for Leray solutions of 3D Navier-Stokes equations
• On time inhomogeneous stochastic Itô equations with drift in $L_{d+1}$