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Harnack inequality for Ornstein–Uhlenbeck type operators

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We prove Harnack type inequalities for non-negative weak solutions in $$(0,T]\times \mathbb {R}^N$$ ( 0 , T ] × R N of parabolic problems related to operators of the type… Click to show full abstract

We prove Harnack type inequalities for non-negative weak solutions in $$(0,T]\times \mathbb {R}^N$$ ( 0 , T ] × R N of parabolic problems related to operators of the type $$L=\hbox {div}\,\left( Q(t,x)\nabla \right) +\langle B(x)+F(t,x),\nabla \rangle $$ L = div Q ( t , x ) ∇ + ⟨ B ( x ) + F ( t , x ) , ∇ ⟩ , where Q is uniformly elliptic, F is bounded, and B is twice differentiable with bounded derivatives.

Keywords: harnack inequality; inequality ornstein; ornstein uhlenbeck; type operators; type; uhlenbeck type

Journal Title: Archiv der Mathematik
Year Published: 2020

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