共查询到20条相似文献,搜索用时 78 毫秒
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We use maximum principle techniques to obtain a Harnack inequality for two-dimensional elliptic operators 相似文献
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We study the Harnack inequality for weak solutions of a class of degenerate parabolic quasilinear PDE $$\begin{aligned} \partial _t u={-}X_i^* A_i(x,t,u,Xu)+ B(x,t,u,Xu), \end{aligned}$$ in cylinders $\Omega \times (0,T)$ where $\Omega \subset M$ is an open subset of a manifold $M$ endowed with control metric $d$ corresponding to a system of Lipschitz continuous vector fields $X=(X_1,\ldots ,X_m)$ and a measure $d\sigma $ . We show that the Harnack inequality follows from the basic hypothesis of doubling condition and a weak Poincaré inequality in the metric measure space $(M,d,d\sigma )$ . We also show that such hypothesis hold for a class of Riemannian metrics $g_\epsilon $ collapsing to a sub-Riemannian metric $\lim _{\epsilon \rightarrow 0} g_\epsilon =g_0$ uniformly in the parameter $\epsilon \ge 0$ . 相似文献
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Moritz Kassmann 《Comptes Rendus Mathematique》2011,349(11-12):637-640
We provide a new formulation of Harnack?s inequality for nonlocal operators. In contrast to previous versions we do not assume harmonic functions to have a sign. The version of Harnack?s inequality given here generalizes Harnack?s classical result from 1887 to nonlocal situations. As a consequence we derive Hölder regularity estimates by an extension of Moser?s method. The inequality that we propose is equivalent to Harnack?s original formulation but seems to be new even for the Laplace operator. 相似文献
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In this paper we prove existence and regularity results for a class of semilinear evolution equations that are satisfied by vector potentials associated with Maxwell’s equations in Carnot groups (connected, simply connected, stratified nilpotent Lie groups). The natural setting for these equations is provided by the so-called Rumin’s complex of intrinsic differential forms. 相似文献
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Potential Analysis - This article presents two types of Hardy’s inequalities for the Heisenberg group. The proofs are mainly based on estimates of the Fourier transform for atomic functions... 相似文献
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In this work, we first prove a generalized version of a parameterized Jordan-type inequality. We then use it to prove the generalized versions of Janous’s inequality and Tsintsifas’s inequality which reduce to two inequalities conjectured by Janous and Tsintsifas as special cases. 相似文献
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Haakan Hedenmalm 《Journal d'Analyse Mathématique》2012,118(2):691-702
We shed new light on Heisenberg??s uncertainty principle in the sense of Beurling, by offering a fundamentally different proof which allows us to weaken the assumptions rather substantially. The new formulation is pretty much optimal, as can be seen from examples. Our arguments involve Fourier and Mellin transforms. We also introduce a version which applies to two given functions. Finally, we show how our approach applies in the higher dimensional setting. 相似文献
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Abstract We study Harnack type properties of quasiminimizers of the
-Dirichlet integral on metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality. We show
that an increasing sequence of quasiminimizers converges locally uniformly to a quasiminimizer, provided the limit function
is finite at some point, even if the quasiminimizing constant and the boundary values are allowed to vary in a bounded way.
If the quasiminimizing constants converge to one, then the limit function is the unique minimizer of the
-Dirichlet integral. In the Euclidean case with the Lebesgue measure we obtain convergence also in the Sobolev norm.
Keywords: Metric space, doubling measure, Poincaré inequality, Newtonian space, Harnack inequality, Harnack convergence theorem
Mathematics Subject Classification (2000): 49J52, 35J60, 49J27 相似文献
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Shouwen Fang 《Geometriae Dedicata》2012,161(1):11-22
In the paper we prove some differential Harnack inequalities for positive solutions of heat equations with potentials when the metric is evolving by the Bernhard List??s flow. We also give some applications of these inequalities. 相似文献
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Sharpened versions of a Kolmogorov’s inequality for sums of independent Bernoulli random variables are proved. 相似文献
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S. K. Godunov 《Computational Mathematics and Mathematical Physics》2013,53(8):1179-1182
Maxwell’s equations, relativistic invariant equations, foundations of difference schemes. 相似文献
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E. D. Nursultanov 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):185-202
Let (X, Y) be a pair of normed spaces such that X ? Y ? L 1[0, 1] n and {e k } k be an expanding sequence of finite sets in ? n with respect to a scalar or vector parameter k, k ∈ ? or k ∈ ? n . The properties of the sequence of norms $\{ \left\| {S_{e_k } (f)} \right\|x\} _k $ of the Fourier sums of a fixed function f ∈ Y are studied. As the spaces X and Y, the Lebesgue spaces L p [0, 1], the Lorentz spaces L p,q [0, 1], L p,q [0, 1] n , and the anisotropic Lorentz spaces L p,q*[0, 1] n are considered. In the one-dimensional case, the sequence {e k } k consists of segments, and in the multidimensional case, it is a sequence of hyperbolic crosses or parallelepipeds in ? n . For trigonometric polynomials with the spectrum given by step hyperbolic crosses and parallelepipeds, various types of inequalities for different metrics in the Lorentz spaces L p,q [0, 1] n and L p,q*[0, 1] n are obtained. 相似文献
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Michele Bartuccelli Guido Gentile James A. Wright 《Applied Mathematics Letters》2013,26(10):1026-1030
We present a class of Hill’s equations possessing explicit solutions through elementary functions. In addition we provide some applications by using some of the paradigmatic systems of classical dynamics, such as the pendulum with variable length. 相似文献
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The representations of the Galilean algebra and its extensions relative to which the system of nonlinear reaction-convection-diffusion equations can be invariant are investigated. The kinds of nonlinearities at which this system is invariant relative to those algebras are determined to within continuous equivalence transformations. 相似文献
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A. A. Muromskaya 《Moscow University Mathematics Bulletin》2017,72(1):31-34
The ruin probability of an insurance company paying dividends according to a barrier strategy with a step barrier function is considered. Upper bounds for the probability of ruin are obtained within the framework of Sparre Andersen and Cramer–Lundberg risk models. 相似文献