共查询到20条相似文献,搜索用时 15 毫秒
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Abstract
We prove existence and uniqueness of a viscosity solution of the Dirichlet problem related to the prescribed Levi mean curvature
equation, under suitable assumptions on the boundary data and on the Levi curvature of the domain. We also show that such
a solution is Lipschitz continuous by proving that it is the uniform limit of a sequence of classical solutions of elliptic
problems and by building Lipschitz continuous barriers.
Keywords: Levi mean curvature, Quasilinear degenerate elliptic PDE’s, Viscosity solutions, Comparison principle, Global Lipschitz estimates 相似文献
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N. A. Kudryashov 《Theoretical and Mathematical Physics》2000,122(1):58-71
We present two hierarchies of ordinary differential equations and give the relations between these hierarchies. We find rational
and special solutions of one hierarchy. Solutions of two differential equations are shown to be essentially transcendental
functions with respect to the integration constants.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 1, pp. 72–87, January, 1999. 相似文献
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In the present paper we explain new Levi conditions of C∞ type for second-order hyperbolic Cauchy problems. Our goal is to explain the special influence of oscillations in the coefficients. It turns out that such oscillations have an essential influence coupled with the asymptotic behavior of characteristics around multiple points. 相似文献
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Journal of Evolution Equations - 相似文献
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A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined
explicitly in Powers and Scheiderer (Adv Geom 1, 71–88, 2001), is a very useful property. It often implies that the quadratic
module is closed; furthermore, it helps settling the Moment Problem, solves the Membership Problem for quadratic modules and
allows applications of methods from optimization to represent nonnegative polynomials. We provide sufficient conditions for
finitely generated quadratic modules in real polynomial rings of several variables to be stable. These conditions can be checked
easily. For a certain class of semi-algebraic sets, we obtain that the nonexistence of bounded polynomials implies stability
of every corresponding quadratic module. As stability often implies the non-solvability of the Moment Problem, this complements
the result from Schmüdgen (J Reine Angew Math 558, 225–234, 2003), which uses bounded polynomials to check the solvability
of the Moment Problem by dimensional induction. We also use stability to generalize a result on the Invariant Moment Problem
from Cimpric et al. (Trans Am Math Soc, to appear). 相似文献
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H. Mejjaoli 《Applicable analysis》2013,92(10):1645-1668
In this article, we introduce a class of nonlinear wave equations associated with the Dunkl operators, we study local and global well-posedness. Next, we establish the linearization of bounded energy solutions in the spirit of Gérard [P. Gérard, Oscillations and concentration effects in semilinear dispersive wave equations, J. Funct. Anal. 141 (1996), pp. 60–98]. The proof uses Strichartz-type inequalities and the energy estimate. 相似文献
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We investigate an initial value problem which is closely related to the Williams-Bjerknes tumour model for a cancer which
spreads through an epithelial basal layer modeled onI ⊂ Z
2. The solution of this problem is a familyp = (p
i(t)), where eachp
i(t)could be considered as an approximation to the probability that the cell situated ati is cancerous at timet. We prove that this problem has a unique solution, it is defined on [0, +∞[, and, for some relevant situations, limt→∞
P
i(t) = 1 for alli ∈ I. Moreover, we study the expected number of cancerous cells at timet. 相似文献
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Sanghyun Cho 《Journal of Mathematical Analysis and Applications》2003,283(2):386-397
Let Ω be a smoothly bounded pseudoconvex domain in and let be a point of finite type. We also assume that the Levi form of bΩ is comparable in a neighborhood of z0. Then we get a quantity which bounds from above and below the Bergman kernel function in a small constant and large constant sense. 相似文献
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We study curve motions based on differential equations. Curve motion equations are classified into two types: adaptive equations (which depend on the choice of coordinate systems) and non-adaptive equations. Examples from both types of equations are studied, and the global existence for these equations is proved based on integral estimates. 相似文献
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F. Feo 《Journal of Evolution Equations》2009,9(3):491-509
In this paper we study a class of parabolic initial boundary value problems relative to an operator whose the prototype is
where W(x) is a smooth function and Z is a constant. We obtain an estimate of the solution comparing it with the solution to a problem relative to the operator
where is the density of Gauss measure, is a function related to g and the data depend only on the time variable and the first space variable. 相似文献
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We use two nonlinear recurrence relations to define the same sequence of polynomials, a sequence resembling the Chebyshev polynomials of the first kind. Among other properties, we obtain results on their irreducibility and zero distribution. We then study the \(2\times 2\) Hankel determinants of these polynomials, which have interesting zero distributions. Furthermore, if these polynomials are split into two halves, then the zeros of one half lie in the interval \((-1,1)\), while those of the other half lie on the unit circle. Some further extensions and generalizations of these results are indicated. 相似文献