共查询到20条相似文献,搜索用时 15 毫秒
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Katsiaryna Krupchyk Werner M. Seiler Jukka Tuomela 《Foundations of Computational Mathematics》2006,6(3):309-351
We consider linear overdetermined systems of partial differential equations.
We show that the introduction of weights classically used for the definition
of ellipticity is not necessary, as any system that is elliptic with respect
to some weights becomes elliptic without weights during its completion to
involution. Furthermore, it turns out that there are systems which are not
elliptic for any choice of weights but whose involutive form is nevertheless
elliptic. We also show that reducing the given system to lower order or to
an equivalent system with only one unknown function preserves ellipticity. 相似文献
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本文讨论了一阶非线性椭圆型复方程组于平面多连通区域上的一类复合边值问题解的先验估计及可解性. 相似文献
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We discuss explicit boundary value problems for solutions of the Fueter equation in which are normally solvable. The results extend to nonlinear first order elliptic systems.
Received: October, 2007, Accepted: February, 2008. 相似文献
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在由光滑Jordan曲线Ω:H(x,y)=0围成的区域Ω中,考虑方程(u)≡A_0H~au_(xx)+2B_0H~βu_(xy)+C_0H~yu_(yy)+au_x+bu_y+cu=0, (1) 对0<λ<1,我们规定以C~(m+λ)(Ω)表示C~m(Ω)中其m阶导数在Ω上满足具有指数λ的Holder条件的那些函数所成的类。我们假设:方程(1)的系数A_0、B_0、C_0、a、b、c∈CC~λ(Ω),H∈C~(2+λ)(Ω),并且c0,常数a、β、r>0。不妨设在Ω中H(x,y)>0,而在Ω上A_0、B_0、C_0均不恒为零。 假设在Ω中B_0~2H~(2β)-A_0C_0H~(a+γ)<0,即方程是椭圆型的。由假设可知2βα+γ。显然,方程(1)在整个边界Ω上呈退化。而以往的许多工作,如丁正中和他的文献中指出的 相似文献
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Fang ainong 《数学年刊B辑(英文版)》1982,3(5):587-594
In this paper we establish the esxistence and uniqueness theorems of a solution of the problem P(|z|=1,Re[z^-nw_z]=0) and H(|z|=1,Re[z^-nw]=0) for the nonlinear system (A):w_{\bar z}=g(z,w,w_z),|g(z,w,w_z^1)-g(z,w,w_z^2)| \leq q_0|w_z^1-w_z^2|,q_0=const.<1,z \in G={|z|<1}.for the problem P,where w(z) \in C_\alpha^1(\bar G),let C_\alpha(g(z,w,t)-g(z,w_1,t_1),\bar G) \leq H_3C_\alpha(w-w_1,\bar G)+H_4C_\alpha(t-t_1,\bar G),H_3,H_4 and C_\alpha(g(z,0,0),\bar G)be the suitable small constants.For the problem H,where w(z) \inW_p^(1)(\bar G),p>2,let |g(z,w,0)| \leq A(z,w)|w|^m+B(z,w),m>1,A(z,w) \in L_p(\bar G) and ||B(z,w)||_{L_p(\bar G)} be the suitable small. 相似文献
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一类无界区域中的椭圆型系统非局部边值问题 总被引:1,自引:0,他引:1
本文讨论了一类在无界区域中的非线性椭圆系统的非局部边值问题。在适当的条件下,相对边值问题解的存在性及其比较定理作了研究。 相似文献
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本文以解析函数的边值问题B的解的存在性为基础,根据它们的先验估计式及利用参数开拓法,导出了满足条件C的多个复变量的一阶拟线性椭圆型复方程组的Riemann-Hilbert边值问题的可解条件,并给出了解的积分表达式. 相似文献
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J. Karátson 《Acta Mathematica Hungarica》2001,93(1-2):115-133
The infinite-dimensional gradient method is applied to the iterative solution of quasilinear elliptic boundary value problems. Earlier results on uniformly monotone problems are extended to a general case within the scope of Hilbert space well-posedness. Linear convergence is proved in Sobolev norm. This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Lynn ERBE Christopher C. TISDELL Patricia J. Y. WONG 《数学学报(英文版)》2007,23(3):549-556
Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions. 相似文献
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Nikolai Tarkhanov 《Complex Analysis and Operator Theory》2007,1(1):115-141
We consider a boundary value problem for an elliptic differential operator of order 2m in a domain
. The boundary of
is smooth outside a smooth manifold Y of dimension 0 ≤ q < n − 1, and
bears edge type singularities along Y . The Lopatinskii condition is assumed to be fulfilled on the smooth part of
. The corresponding spaces are weighted Sobolev spaces
, and this allows one to define ellipticity of weight γ for the problem. The resolvent of the problem is assumed to possess
rays of minimal growth. The main result says that if there are rays of minimal growth with angles between neighbouring rays
not exceeding π(γ + 2m)/n, then the root functions of the problem are complete in
. In the case of second order elliptic equations the results remain true for all domains with Lipschitz boundary.
Communicated by Michael Shapiro.
Submitted: May 24, 2006; Accepted: June 15, 2006 相似文献
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§1.IntroductionThedomainoptimizationproblemisakindofshapeoptimizationproblem.Specifical-ly,wewanttofindadomain(whichiscaledop... 相似文献
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We study solvability of boundary value problems for odd order differential equations in time variables. The presence of a discontinuous alternating coefficient is a peculiarity of these equations. We prove existence and uniqueness theorems for the regular solutions of such an equation, i.e. those that have all Sobolev generalized derivatives entering the equation under study. 相似文献
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讨论一类非齐次非线性椭圆边界值问题.利用极大值原理证明了该问题解的梯度估计.作为它的应用得到了解的效率比估计. 相似文献
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