共查询到20条相似文献,搜索用时 15 毫秒
1.
ho Lijiang 《东北数学》1995,(4)
ExistenceTheoremofGlobalSolutionsforMonge-AmpereEquationhoLijiang(鹿立江)(TianjinUniversityofFinanceandEconomics,Tianjin,300222)... 相似文献
2.
3.
In this note we consider the first boundary value problem for a general parabolic Monge-Ampere equation u_t - log det(D_{ij}u) = f(x, t, u,D_2u) in Q, \quad u = φ(x, t) on ∂, Q It is proved that there exists a unique convex in x solution to the problem from C^{1+β,2+β/2}(\overline{Q}) under certain structure aod smoothness conditions (H3) - (H7). 相似文献
4.
Generalized Solution of the First Boundary Value Problem for Parabolic Monge-Ampere Equation 下载免费PDF全文
The existence and uniqueness of generalized solution to the first boundary value problem for parabolic Monge-Ampère equation - ut det D²_xu = f in Q = Ω × (0, T], u = φ on ∂_pQ are proved if there exists a strict generalized supersolution u_φ, where Ω ⊂ R^n is a bounded convex set, f is a nonnegative bounded measurable function defined on Q, φ ∈ C(∂_pQ), φ(x, 0) is a convex function in \overline{\Omega}, ∀x_0 ∈ ∂Ω, φ(x_0, t) ∈ C^α([0, T]). 相似文献
5.
The Geometric Measure Theoretical Characterization of Viscosity Solutions to Parabolic Monge-Ampere Type Equation 下载免费PDF全文
By an involved approach a geometric measure theory is established for parabolic Monge-Ampère operator acting on convex-monotone functions, the theory bears complete analogy with Aleksandrov's classical ones for elliptic Monge-Ampère operator acting on convex functions. The identity of solutions in weak and viscosity sense to parabolic Monge-Ampère equation is proved. A general result on existence and uniqueness of weak solution to BVP for this equation is also obtained. 相似文献
6.
Alexandre Boritchev 《Geometric And Functional Analysis》2013,23(6):1730-1771
We consider the non-homogeneous generalised Burgers equation $$\frac{\partial u}{\partial t} + f'(u)\frac{\partial u}{\partial x} -\nu \frac{\partial^2 u}{\partial x^2} = \eta,\ t \geq 0,\ x \in S^1.$$ Here f is strongly convex and satisfies a growth condition, ν is small and positive, while η is a random forcing term, smooth in space and white in time. For any solution u of this equation we consider the quasi-stationary regime, corresponding to ${t \geq T_1}$ , where T 1 depends only on f and on the distribution of η. We obtain sharp upper and lower bounds for Sobolev norms of u averaged in time and in ensemble. These results yield sharp upper and lower bounds for natural analogues of quantities characterising the hydrodynamical turbulence. All our bounds do not depend on the initial condition or on t for ${t \geq T_1}$ , and hold uniformly in ν. Estimates similar to some of our results have been obtained by Aurell, Frisch, Lutsko and Vergassola on a physical level of rigour; we use an argument from their article. 相似文献
7.
Lijiang Lu 《偏微分方程(英文版)》1996,9(2):97-102
In this paper, we discuss the regularity of the weak solutions and the existence of the classical solutions for Monge-Ampère equations on the bounded convex domains possessing uniform parabolic support. This paper improves the conclusion of [1]. 相似文献
8.
Consider the image of the MongeAmpère operatoracting on bounded functions, defined on a compact Kählermanifold, whose sum with the local Kähler potential isplurisubharmonic. It is shown that a nonnegative Borel measurebelongs to this image if and only if it belongs to the imagelocally. In particular, those measures form a convex set. 相似文献
9.
Gang TIAN 《数学年刊B辑(英文版)》2017,38(2):687-694
The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate,and consequently,a C2,α-estimate,for complex MongeAmpere equations in the conic case.This C2,α-estimate was used by Jeffres-MazzeoRubinstein in their proof of the existence of K(a)hler-Einstein metrics with conic singularities. 相似文献
10.
11.
P. L. Lions 《Annali di Matematica Pura ed Applicata》1985,142(1):263-275
Summary
We consider real Monge-Ampère equations and we present two new properties of these equations. First, we show the existence of the «first eigenvalue of Monge-Ampère equation» i.e. we show the existence of a positive constant possessing all the properties of the first eigenvalue of a 2-nd order elliptic operator (positivity, uniqueness of the eigenfunction, maximum principle, bifurcation...).The second property concerns variational characterisations of solutions. Both properties are closely related to similar properties of the general class of Hamilton-Jacobi-Bellman equations. 相似文献
12.
On Another Kind of Parabolic Monge-Ampere Equation:the Existence,Uniqueness and Regularity of the Vi
Wang Rouhuai 《东北数学》1994,(4)
On Another Kind of Parabolic Monge-Ampere Equation:the Existence,Uniqueness and Regularity of the Viscosity SolutionWangRouhu... 相似文献
13.
Kevin Burke 《代数通讯》2013,41(1):265-297
Crawley-Boevey's concept of a character (a notion derived from Schofield's Sylvester rank functions) is extended so that characters with different image sets and classes may be analysed. A method of passing from these generalised characters to theories of modules is given and a converse technique is seen to be possible in certain cases. We consider in depth what happens when the character image is taken to be the ordinals with addition taken to be the Cantor sum. In particular we define a process whereby any Σ-pure-injective module satisfying a reasonable criterion can be assigned a unique ordinal character. 相似文献
14.
Jonathan Schilhan 《Mathematical Logic Quarterly》2019,65(4):479-489
15.
The SkolemMahlerLech theorem states that if f(n)is a sequence given by a linear recurrence over a field of characteristic0, then the set of m such that f(m) is equal to 0 is the unionof a finite number of arithmetic progressions in m 0 and afinite set. We prove that if X is a subvariety of an affinevariety Y over a field of characteristic 0 and q is a pointin Y, and is an automorphism of Y, then the set of m such thatm(q) lies in X is a union of a finite number of complete doubly-infinitearithmetic progressions and a finite set. We show that thisis a generalisation of the SkolemMahlerLech theorem. 相似文献
16.
Peter M. Schuster 《Mathematical Logic Quarterly》2000,46(1):125-134
We investigate how nonstandard reals can be established constructively as arbitrary infinite sequences of rationals, following the classical approach due to Schmieden and Laugwitz. In particular, a total standard part map into Richman's generalised Dedekind reals is constructed without countable choice. 相似文献
17.
N. M. Ivochkina 《Journal of Mathematical Sciences》1990,52(1):2861-2863
In this note we describe a geometric problem leading to Monge-Ampere type operators. Some variational problems and theorems on their solvability are formulated.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 167, pp. 186–189, 1988. 相似文献
18.
Pierre-Louis Lions 《manuscripta mathematica》1983,41(1-3):1-43
In this paper we study the real Monge-Arapère equations: det(D2u)= f(x) in 0, u convex in 0, u=0 on 0, and we introduce a new method for solving these equations which enables us to show the existence of regular solutions. This method uses only p.d.e. techniques and does not use any geometrical results. Furthermore, it enables us to solve quasilinear Monge-Ampère equations. 相似文献
19.
20.