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As a continuation to [F.-Y. Wang, Harnack inequality and applications for stochastic generalized porous media equations, Ann. Probab. 35 (2007) 1333-1350], where the Harnack inequality and the strong Feller property are studied for a class of stochastic generalized porous media equations, this paper presents analogous results for stochastic fast-diffusion equations. Since the fast-diffusion equation possesses weaker dissipativity than the porous medium one does, some technical difficulties appear in the study. As a compensation to the weaker dissipativity condition, a Sobolev-Nash inequality is assumed for the underlying self-adjoint operator in applications. Some concrete examples are constructed to illustrate the main results. 相似文献
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We consider viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on a Riemannian manifold M with the sectional curvature bounded from below by −κ for κ≥0. In the elliptic case, Wang and Zhang [24] recently extended the results of [5] to nonlinear elliptic equations in nondivergence form on such M, where they obtained the Harnack inequality for classical solutions. We establish the Harnack inequality for nonnegative viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on M. The Harnack inequality of nonnegative viscosity solutions to the elliptic equations is also proved. 相似文献
4.
Roger Chen 《Proceedings of the American Mathematical Society》2001,129(7):2163-2173
In this paper we consider a non-self-adjoint evolution equation on a compact Riemannian manifold with boundary. We prove a Harnack inequality for a positive solution satisfying the Neumann boundary condition. In particular, the boundary of the manifold may be nonconvex and this gives a generalization to a theorem of Yau.
5.
We prove a Harnack inequality for Dirichlet eigenfunctions of abelian homogeneous graphs and their convex subgraphs. We derive lower bounds for Dirichlet eigenvalues using the Harnack inequality. We also consider a randomization problem in connection with combinatorial games using Dirichlet eigenvalues. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 247–257, 2000 相似文献
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Fausto Ferrari 《Mathematische Nachrichten》2006,279(8):815-830
In this note, we prove a Harnack inequality for two‐weight subelliptic p ‐Laplace operators together with an upper bound of the Harnack constant associated with such inequality. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
We present graphs that satisfy the uniform elliptic Harnack inequality, for harmonic functions, but not the stronger parabolic one, for solutions of the discrete heat equation. It is known that the parabolic Harnack inequality is equivalent to the conjunction of a volume regularity and a L
2 Poincaré inequality. The first example of graph satisfying the elliptic but not the parabolic Harnack inequality is due to M. Barlow and R. Bass. It satisfies the volume regularity and not the Poincaré inequality. We construct another example that does not satisfy the volume regularity. 相似文献
8.
Richard F. Bass Moritz Kassmann 《Transactions of the American Mathematical Society》2005,357(2):837-850
We consider harmonic functions with respect to the operator
Under suitable conditions on we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator is allowed to be anisotropic and of variable order.
Under suitable conditions on we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator is allowed to be anisotropic and of variable order.
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Minghua Lin 《Linear and Multilinear Algebra》2017,65(10):2024-2030
We revisit and comment on the Harnack type determinantal inequality for contractive matrices obtained by Tung in the nineteen sixties and give an extension of the inequality involving multiple positive semidefinite matrices . 相似文献
10.
Harnack inequality for some classes of Markov processes 总被引:3,自引:0,他引:3
In this paper we establish a Harnack inequality for nonnegative harmonic functions of some classes of Markov processes with jumps.
Mathematics Subject Classification (2000): Primary 60J45, 60J75, Secondary 60J25.This work was completed while the authors were in the Research in Pairs program at the Mathematisches Forschungsinstitut Oberwolfach. We thank the Institute for the hospitality.The research of this author is supported in part by NSF Grant DMS-9803240.The research of this author is supported in part by MZT grant 0037107 of the Republic of Croatia. 相似文献
11.
Jiayong WU 《数学年刊B辑(英文版)》2020,41(2):267-284
This paper deals with constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation ωt = ?ω + aωln ω on closed manifolds. A new interpolated Harnack inequality for ωt = ?ω-ωln ω +εRω on closed surfaces under ε-Ricci flow is also derived. Finally, the author proves a new differential Harnack inequality for ωt= ?ω-ωln ω under Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponential functions,... 相似文献
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Chow Bennett 《偏微分方程(英文版)》1998,11(2):137-140
We establish a one-parameter family of Harnack inequalities connecting Li and Yau's differential Harnack inequality for the heat equation to Hamilton's Harnack inequality for the Ricci flow on a 2-dimensional manifold with positive scalar curvature. 相似文献
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Shaoqin ZHANG 《Frontiers of Mathematics in China》2016,11(2):461-496
Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F.-Y. Wang [Ann. Probab., 2012, 42(3): 994–1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non-Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established. 相似文献
14.
Mikhail Surnachev 《Journal of Differential Equations》2010,248(8):2092-2129
In this paper we generalize the recent result of DiBenedetto, Gianazza, Vespri on the Harnack inequality for degenerate parabolic equations to the case of a weighted p-Laplacian type operator in the spatial part. The weight is assumed to belong to the suitable Muckenhoupt class. 相似文献
15.
Qihua Ruan 《Journal of Mathematical Analysis and Applications》2007,329(2):1430-1439
For any complete manifold with nonnegative Bakry-Emery's Ricci curvature, we prove the gradient estimate of L-harmonic function. As application, we use this gradient estimate to deduce the localized version of the Harnack inequality for L-harmonic operator and some Liouville properties of positive or bounded L-harmonic function. 相似文献
16.
Derek Booth Jack Burkart Xiaodong Cao Max Hallgren Zachary Munro Jason Snyder Tom Stone 《分析论及其应用》2019,35(2):192-204
This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead-Segel equation on R^n.We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation,including deriving a classical Harnack inequality and characterizing standing solutions and traveling wave solutions. 相似文献
17.
Qingbo Huang 《Transactions of the American Mathematical Society》1999,351(5):2025-2054
In this paper we prove the Harnack inequality for nonnegative solutions of the linearized parabolic Monge-Ampère equation
on parabolic sections associated with , under the assumption that the Monge-Ampère measure generated by satisfies the doubling condition on sections and the uniform continuity condition with respect to Lebesgue measure. The theory established is invariant under the group , where denotes the group of all invertible affine transformations on .
18.
We prove local and global regularity for the positive solutions of a quasilinear variational degenerate equation, assuming minimal hypothesis on the coefficients of the lower order terms. As an application we obtain Hölder continuity for the gradient of solutions to nonvariational quasilinear equations. 相似文献
19.
We establish the Harnack inequality for advection-diffusion equations with divergence-free drifts by adapting the classical Moser technique to parabolic equations with drifts with regularity lower than the scale invariant spaces. 相似文献
20.
Lijing Sun 《分析论及其应用》2008,24(3):247-259
We prove a uniform Harnack inequality for nonnegative solutions of ΔG
u − μu = 0, where ΔG is a sublaplacian, μ is a non-negative Radon measure and satisfying scale-invariant Kato condition.
相似文献