Harnack inequalities and Hölder estimates for master equations

2018/06/26 by Animesh Biswas, Biswas, A., Marta De León-Contreras +3
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1806.10072

Abstract

We study master equations of the form (∂_t+L)^su=f \hboxin~ℝ×Ω where L is a divergence form elliptic operator and Ω⊆ℝⁿ. These are nonlocal equations of order 2s in space and s in time that take into account the values of u everywhere in Ω and for past times. We show parabolic interior and boundary Harnack inequalities and local parabolic Hölder continuity of solutions. To this end, we prove a characterization of fractional powers of parabolic operators ∂_t+L with a degenerate parabolic extension problem.

Related

• Regularity estimates for nonlocal space-time master equations in bounded domains
• Hölder Continuity and Harnack estimate for non-homogeneous parabolic equations
• Fractional elliptic equations in nondivergence form: definition, applications and Harnack inequality
• The Harnack inequality for a class of nonlocal parabolic equations
• Harnack's inequality for fractional nonlocal equations