共查询到20条相似文献,搜索用时 0 毫秒
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N. B. Willms G. M. L. Gladwell D. Siegel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1994,45(4):556-579
In this paper we study various overdetermined boundary value problems for elliptic equations. In particular, we introduce overdetermined problems for the Saint-Venant equation whose only solution domain is the concentric circular annulus. The proofs depend on a generalisation of the reflection method of James Serrin. We then use these results to generalise, to the case of doubly connected ring domains, the recent work of L. Payne and G. Philippin for the Stekloff eigenvalue problem: we present overdetermining conditions which permit solution only when the domain is a concentric circular annulus. Here, the proof employs an integral characterisation of the annulus by harmonic functions. 相似文献
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Ilaria Fragalà 《Journal of Differential Equations》2008,245(5):1299-1322
We consider semilinear elliptic Dirichlet problems in bounded domains, overdetermined with a Neumann condition on a proper part of the boundary. Under different kinds of assumptions, we show that these problems admit a solution only if the domain is a ball. When these assumptions are not fulfilled, we discuss possible counterexamples to symmetry. We also consider Neumann problems overdetermined with a Dirichlet condition on a proper part of the boundary, and the case of partially overdetermined problems on exterior domains. 相似文献
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L. E. Payne G. A. Philippin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(6):864-873
Summary In this paper we study various overdetermined problems involving harmonic functions. In particular, we show that if the second eigenfunctionu
2 of the Stekloff eigenvalue problem in a bounded simply connected plane domain has a constant value of u
2 on , then is a disk
Résumé Cet article est consacré à l'étude de certains problèmes surdéterminés pour des fonctions harmoniques. En particulier, nous montrons que si le gradient de la seconde fonction propre du problème de Stekloff défini dans un domaine borné, simplement connexe du plan, a son module constant sur la frontière , alors est nécessairement un disque.相似文献
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Allan C. Peterson 《Journal of Mathematical Analysis and Applications》1975,52(3):573-582
In this paper we are concerned with proving comparison theorems, under various assumptions, for the (p, q)-boundary value problem for the nth order nonlinear differential equation and the linear differential equation lny = (?1)qk(t)y, where ln is the classical nth order linear operator with leading coefficient one. 相似文献
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Genqian Liu 《Journal of Differential Equations》2007,233(2):585-600
The well-known Schiffer conjecture saying that for a smooth bounded domain Ω⊂Rn, if there exists a positive Neumann eigenvalue such that the corresponding Neumann eigenfunction u is constant on the boundary of Ω, then Ω is a ball. In this paper, we shall prove that the Schiffer conjecture holds if and only if the third order interior normal derivative of the corresponding Neumann eigenfunction is constant on the boundary. We also prove a similar result to the Berenstein conjecture for the overdetermined Dirichlet eigenvalue problem. 相似文献
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Genqian Liu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):3943-3952
We prove the radial symmetry of the solutions of second-order nonlinear elliptic equations for overdetermined Dirichlet and Neumann boundary value problems. In addition, a global uniqueness theorem of Holmgren type is given for nonlinear elliptic equations. 相似文献
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Hans G. Kellerer 《Probability Theory and Related Fields》1984,67(4):399-432
Summary Given topological spaces X
1, ..., X
n with product space X, probability measures
i on X
i together with a real function h on X define a marginal problem as well as a dual problem. Using an extended version of Choquet's theorem on capacities, an analogue of the classical duality theorem of linear programming is established, imposing only weak conditions on the topology of the spaces X
i and the measurability resp. boundedness of the function h. Applications concern, among others, measures with given support, stochastic order and general marginal problems. 相似文献
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Several duality formulation and theorems, and relationship between them in fuzzy programming problems have been studied in literature by various authors under different conditions. In this paper, by considering a partial order relation on the set of fuzzy numbers, and convexity with differentiability of fuzzy mappings, we discuss duality theorems and relationships between them in fuzzy optimization problems with fuzzy coefficients. 相似文献
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This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type , where δ>0 is the ratio of odd positive integers, {pn} and {qn} are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions. 相似文献
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In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants. 相似文献
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We modify and extend proofs of Serrin’s symmetry result for overdetermined boundary value problems from the Laplace-operator
to a general quasilinear operator and remove a strong ellipticity assumption in Philippin (Maximum principles and eigenvalue
problems in partial differential equations (Knoxville, TN, 1987), Longman Sci. Tech., Pitman Res. Notes Math. Ser., Harlow,
175, pp. 34–48, 1988) and a growth assumption in Garofalo and Lewis (A symmetry result related to some overdetermined boundary
value problems, Am. J. Math. 111, 9–33, 1989) on the diffusion coefficient A, as well as a starshapedness assumption on Ω in Fragalà et al. (Overdetermined boundary value problems with possibly degenerate
ellipticity: a geometric approach. Math. Zeitschr. 254, 117–132, 2006). 相似文献