Phragmén-Lindelöf conditions for graph varieties

For P_m ∈ ?[z₁, …, z_n], homogeneous of degree m we investigate when the graph of P_m in ?ⁿ⁺¹ satisfies the Phragmén-Lindelöf condition PL(?ⁿ⁺¹, log), or equivalently, when the operator $i{\partial \over \partial_{x_{n+1}}}+P_{m}(D)$ admits a continuous solution operator on C^∞(?ⁿ⁺¹). This is shown to happen if the varieties V_+- ? {z ∈ ?ⁿ: P_m(z) = ±1} satisfy the following Phragmén-Lindelöf condition (SPL): There exists A ≥ 1 such that each plurisubharmonic function u on V_+- satisfying u(z) ≤ ¦z¦+ o(¦z¦) on V_+- and u(x) ≤ 0 on V_+- ∩ ?ⁿ also satisfies u(z) A¦ Im z¦ on V_+-. Necessary as well as sufficient conditions for V_+- to satisfy (SPL) are derived and several examples are given.     

Phragmén-Lindelöf theorems for second-order quasilinear elliptic equations

Analogues are formulated of the well-known, in the theory of analytic functions, Phragmen-Lindelöf theorem for the gradients of solutions of a broad class of quasilinear equations of elliptic type. Examples are given illustrating the accuracy of the results obtained for the gradients of solutions of the equations of the form div(|U|^–2u)=f(x, u, u), where f(x, u, u) is a function locally bounded in ²ⁿ⁺¹. f(x, 0, u)=0, uf(x, u, u) c¦u¦1+q(1+ ¦u|), > 1, c > 0, q > 0, is an arbitrary real number, and n >- 2. The basic role in the technique employed in the paper is played by the apparatus of capacitary characteristics.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1376–1381, October, 1992.The author sincerely appreciates E. M. Landis's permanent attention and numerous useful discussions.     

Existence of a Phragmén-Lindelöf function and certain quasianalyticity conditions

Let. The positive harmonic functions in the domain, vanishing on E, form a cone. It is known that. It is proved in this note that if is the distance from the point x to E). For n=1 one traces the relationship between a problem regarding dim and the question of the existence of a charge of finite variation with support on E and such that its Fourier transform vanishes on an interval. In the case n=1 it is also proved that from there follows dim=2.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 97–108, 1983.     

The algebraic surfaces on which the classical Phragmén-Lindelöf theorem holds

Let V be an algebraic variety in . We say that V satisfies the strong Phragmén-Lindelöf property (SPL) or that the classical Phragmén-Lindelöf Theorem holds on V if the following is true: There exists a positive constant A such that each plurisubharmonic function u on V which is bounded above by |z|+o(|z|) on V and by 0 on the real points in V already is bounded by A| Im z|. For algebraic varieties V of pure dimension k we derive necessary conditions on V to satisfy (SPL) and we characterize the curves and surfaces in which satisfy (SPL). Several examples illustrate how these results can be applied.     

Algebraic varieties on which the classical Phragmén-Lindelöf estimates hold for plurisubharmonic functions

Algebraic varieties V are investigated on which the natural analogue of the classical Phragmén-Lindel?f principle for plurisubharmonic functions holds. For a homogeneous polynomial P in three variables it is shown that its graph has this property if and only if P has real coefficients, no elliptic factors, is locally hyperbolic in all real characteristics, and the localizations in these characteristics are square-free. The last condition is shown to be necessary in any dimension. Received July 23, 1998     

Zum Phragmén-Lindelöfschen Prinzip bei partiellen Differentialgleichungen

Ohne Zusammenfassung     

Regularitätsfragen beim Phragmén-Lindelöfschen Prinzip für elliptische Differentialgleichungen

Ohne Zusammenfassung     

椭圆型方程广义解的Phragmén-Lindelf原理

设G是E~n中的无界连通区域,在适当条件下对一类椭圆型方程广义解证明Phragmén-Lindel(?)f原理成立。     

广义带形区域中的Phragmén-Lindel?f型定理

该文给出了广义带形区域中的Phragmén-Lindel?f型定理,所得结果推广了邓冠铁和Aikawa在带型区域中的相关结论.     

二元热传导方程的Phragmén-Lindel?f型二择一结果

考虑了二元热传导方程在半无穷区域上解的渐近性质,其中在柱体的侧面上施加局部非齐次Neumann条件.这种条件模拟了柱体侧面上的绝热材料受到局部破坏的情形.利用微分不等式技术和能量分析的方法,得到了热传导模型的Phragmén-Lindel?f型二择一结果.     

On an inequality of Levinson of the Phragmèn-Lindelöf type

In this paper a new proof, based on Džrbašjan's characterization of H^p-spaces in a half-plane, of an integral inequality of Levinson of the Phragmèn-Lindelöf type is presented.     

多重次调和函数的一个Phragmén-Lindel(o)f定理

该文给出了CN中锥上关于多重次调和函数的一个Phragmé-Lindel(o)f定理,从而推广了文献[8]的一个结论.     

Phragmén-Lindel(o)f Alternative Result of the Forchheimer Equations

This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder.Using the energy estimation method and th...     

Stokes流动中的Phragmén-Lindelf型及其连续相关性的结果

就三维半无限柱体上的Stokes流动,研究边端效应的渐近性质.柱体水平面上的速度满足均匀的Dirichlet条件时,发现问题的解,随柱体有限端的距离,或呈指数增长,或呈指数衰减.最后讨论了方程参数的摄动影响.     

On the Phragmén–Lindelöf Indicator for Random Entire Functions

We establish that, for the majority of entire functions of finite order, their generalized Phragmén–Lindelöf indicators are identically equal to constants.     

Stokes 流动中的 Phragmén-Lindel(o)f型及其连续相关性的结果

就三维半无限柱体上的Stokes流动,研究边端效应的渐近性质.柱体水平面上的速度满足均匀的Dirichlet条件时,发现问题的解,随柱体有限端的距离,或呈指数增长,或呈指数衰减.最后讨论了方程参数的摄动影响.     

Phragmén–Lindelöf alternative and continuous dependence-type results for the thermoelasticity of type III

In this article, equations of thermoelasticity of type III in three-dimensional cylindrical domain are studied. We prove a Phragmén–Lindelöf alternative result, i.e. the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity. In the decay case, the authors indicate how to bound explicitly the total energy in terms of data. The continuous dependence of the solutions on the coefficient ρ is also proved in this article.