LAUSR

Harnack inequality for Ornstein–Uhlenbeck type operators

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0 Published in 2020 at "Archiv der Mathematik"

DOI: 10.1007/s00013-019-01429-z

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… read more here.

Keywords: harnack inequality; inequality ornstein; ornstein uhlenbeck; type operators ... See more keywords

Harnack inequality and gradient estimate for G-SDEs with degenerate noise

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0 Published in 2021 at "Science China Mathematics"

DOI: 10.1007/s11425-020-1784-0

Abstract: In this paper, the Harnack inequalities for $G$-SDEs with degenerate noise are derived by method of coupling by change of measure. Moreover, the gradient estimate for the associated nonlinear semigroup $\bar{P}_t$ $$|\nabla \bar{P}_t f|\leq c(p,t)(\bar{P}_t… read more here.

Keywords: degenerate noise; gradient estimate; sdes degenerate; harnack inequality ... See more keywords

Harnack inequality for quasilinear elliptic equations on Riemannian manifolds

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0 Published in 2018 at "Journal of Differential Equations"

DOI: 10.1016/j.jde.2017.10.003

Abstract: Abstract We study viscosity solutions to degenerate and singular elliptic equations div ( F ′ ( | ∇ u | ) | ∇ u | ∇ u ) = h of p-Laplacian type on Riemannian… read more here.

Keywords: harnack inequality; inequality quasilinear; elliptic equations; riemannian manifolds ... See more keywords

Harnack inequality and pinching estimates for anisotropic curvature flow of hypersurfaces

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0 Published in 2018 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2018.03.062

Abstract: Abstract We obtain a differential Harnack inequality for anisotropic curvature flow of convex hypersurfaces in Euclidean space with its speed given by a curvature function of homogeneity degree one in a certain class, and restrictions… read more here.

Keywords: harnack inequality; curvature flow; anisotropic curvature; curvature ... See more keywords

Local Aronson-Bénilan gradient estimates and Harnack inequality for the porous medium equation along Ricci flow

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0 Published in 2018 at "Communications on Pure and Applied Analysis"

DOI: 10.3934/cpaa.2018093

Abstract: In this paper, we prove some new local Aronson-Benilan type gradient estimates for positive solutions of the porous medium equation \begin{document}$u_{t}=Δ u^{m}, m>1$ \end{document} coupled with Ricci flow, assuming that the Ricci curvature is bounded.… read more here.

Keywords: gradient estimates; harnack inequality; local aronson; ricci flow ... See more keywords