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Andrew Acker 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1978,29(3):395-408
In the class of all strip-like regions (Fig. 1) satisfying a certain condition involving weighted areas, we determine (in the sense of existence, uniqueness, and characterization) the region with the least capacitance.
These results were presented at the conference on the numerical treatment of differential equations with special consideration of free-boundary problems, Mathematisches Forschungsinstitut Oberwolfach, 1.5.1977. 相似文献
Zusammenfassung Unter allen streifenartigen Gebieten (Fig. 1) die ein bestimmte Bedingung betreffend gewichteter Flächen erfüllen, bestimmen wir (im Sinne von Existenz, Eindeutigkeit und Charakterisierung) dasjenige mit kleinster Kapazität.
These results were presented at the conference on the numerical treatment of differential equations with special consideration of free-boundary problems, Mathematisches Forschungsinstitut Oberwolfach, 1.5.1977. 相似文献
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In [6], T. I. Vogel studied a free boundary problem originating in the galvanization process. He showed that if the given boundary Γ* is starlike or convex, then so is the free boundary solution Γ. Our purpose is to generalize Vogel's second result by showing (under certain assumptions) that Γ cannot have more (local) maxima or minima (relative to a given direction) than Γ*; also that Γ cannot have more inflection points or greater total curvature than Γ*. The author has already proven analogous results for the Bernoulli free boundary problem in [1], [2] and [3]. 相似文献
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S. Challal 《Journal of Mathematical Analysis and Applications》2009,355(2):700-707
We prove local interior and boundary Lipschitz continuity of solutions of a free boundary problem involving the p-Laplacian. 相似文献
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E. V. Remizova 《Journal of Mathematical Sciences》1989,45(3):1163-1172
One considers the Dirichlet problem for the equation u=(u), where is the Heaviside function. Under special assumptions one constructs the solution of this problem with convex and smooth level surfaces and, in particular, with a regular free surface, which coincides with the set of level zero. One proves the solvability in the small of the problem in the neighborhood of the constructed regular solution under perturbations of the boundary condition and a smooth boundary of the domain .Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 72–83, 1986. 相似文献
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Let u be the Newtonian potential of a real analytic distribution in an open set Ω. In this paper we assume u is analytically
continuable from the complement of Ω into some neighborhood of a point x0 ∈ ∂Ω, and we study conditions under which the analytic continuation implies that ∂Ω is a real analytic hypersurface in some
neighborhood of x0. 相似文献
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Xiangsheng Xu 《Rendiconti del Circolo Matematico di Palermo》1991,40(1):69-101
Existence of a weak solution is established for the first boundary value problem for the equation (c(u))
t
=(φ(u
x
)
x
in the case wherec′(x), φ′(x) may oscillate near zero,c′(x), φ′(x) may be unbounded above, andc′(x), φ′(x) may not be bounded away from zero asx→0. Some regularity properties of the wea, solution are also obtained. 相似文献
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Summary When two immiscible fluids in a porous medium are in contact with one another, an interface is formed and the movement of
the fluids results in a free boundary problem for determining the location of the interface along with the pressure distribution
throughout the medium. The pressure satisfies a nonlinear parabolic partial differential equation on each side of the interface
while the pressure and the volumetric velocity are continuous across the interface. The movement of the interface is related
to the pressure through Darcy’s law. Two kinds of boundary conditions are considered. In Part I the pressure is prescribed
on the known boundary. A weak formulation of the classical problem is obtained and the existence of a weak solution is demonstrated
as a limit of a sequence of classical solutions to certain parabolic boundary value problems. In Part II the same analysis
is carried out when the flux is specified on the known boundary, employing special techniques to obtain the uniform parabolicity
of the sequence of approximating problems.
Entrata in Redazione il 29 novembre 1975.
This research was supported in part by the National Science Foundation, the Senior Fellowship Program of the North Atlantic
Treaty Organization, the Italian Consiglio Nazionale delle Ricerche, and the Texas Tech. University. 相似文献
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Gunduz Caginalp 《Advances in Applied Mathematics》1984,5(4):476-488
A free boundary problem with a moving source is considered. The existence of a critical velocity, above which a fault line occurs, is known experimentally in welding. One possible explanation has been the formation of a teardrop-shaped weld pool with a sharp vertex at the tail end. It is proved that such a singularity cannot occur within a reasonable two-dimensional model. The model includes physical effects due to discontinuous diffusivities, convection terms, and deviations in the interfacial temperature due to terms such as curvature and linear dynamics. 相似文献
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G. A. Philippin 《Mathematical Methods in the Applied Sciences》1990,12(5):387-392
Let Ωi ? ?N, i = 0, 1, be two bounded separately star-shaped domains such that $ \Omega _0 \supset \bar \Omega _1 $. We consider the electrostatic potential u defined in $ \Omega : = \Omega _0 \backslash \bar \Omega _1 $: The geometry of the two boundary components Γ0 and Γ1 is not given, but instead the electrostatic potential u is supposed to satisfy the further boundary conditions Using a best possible maximum principle, we show that this free boundary problem has a unique solution which is radially symmetric. 相似文献
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Joachim Escher Gieri Simonett 《NoDEA : Nonlinear Differential Equations and Applications》1995,2(4):463-510
This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surface moving under the influence of gravity. The laminar flow is governed by Darcy's law.We prove existence of a unique maximal classical solution, using methods from the theory of maximal regularity, analytic semigroups, and Fourier multipliers. Moreover, we describe a state space which can be considered as domain of parabolicity for the problem under consideration.Supported by Schweizerischer Nationalfonds 相似文献
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Maria Athanassenas 《manuscripta mathematica》1992,76(1):5-19
We prove existence and regularity of capillary surfaces between two parallel hyperplanes in ℝn. By geometrical arguments we also derive some properties of the minimizers of the functional related to the problem. 相似文献
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In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz
and the free boundary is analytic away from a singular set with Hausdorff dimension at most n − 8. 相似文献
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易法槐 《应用数学学报(英文版)》1998,14(1):48-57
1.IntroductionSuperconductorsofTypeIarematerialswhicharecapableofchangingfromthephaseofbeingnormalconductorstoaphasewherethereisnoresistancetothemotionoffreeelections.InnormalconductorphasethenormalizedMaxwellequations(neglectingdisplacementcurrents)aretogetherwithOhm'slawj~acEwhereuistheelectricconductivity.InasuperconductingphaseOhm'slawisnolongervalidandMaxwell'sequationsaresupplemelltedbytheGinzburg-Landaufieldequationsll].Underisothermalconditions,thechangeofphasefromsuperconductingto… 相似文献
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