共查询到20条相似文献,搜索用时 0 毫秒
1.
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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Yu. N. Subbotin N. I. Chernykh 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):142-159
We consider boundary value problems in a disk and in a ring for homogeneous equations with the Laplace operator of the first and second orders. Solutions are represented in terms of bases of harmonic wavelets in Hardy spaces of harmonic functions in a disk and in a ring, which were constructed earlier. 相似文献
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We consider several elliptic boundary value problems for which there is an overspecification of data on the boundary of the domain. After reformulating the problems in an equivalent integral form, we use the alternate integral formulation to deduce that if a solution exists, then the domain must be an N-ball. Various Green's functions and classical boundary value problems of second, fourth and higher order are included among the problems considered here. 相似文献
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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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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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In this paper we investigate two classes of overdetermined initial and boundary value problems of parabolic type. Under appropriate assumptions we conclude that the solutions u( x , t) of the considered problems must be radially symmetric, which implies radial symmetry of the boundary configuration. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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A. A. Illarionov 《Computational Mathematics and Mathematical Physics》2008,48(6):996-1000
A stationary system of Stokes and Navier-Stokes equations describing the flow of a homogeneous incompressible fluid in a bounded domain is considered. The vector of the flow velocity and a finite number of nonlocal conditions are defined at a part of the domain boundary. It is proved that, in the linear case, the problem has at least one stable solution. In the nonlinear case, the local solvability of the problem is proved. 相似文献
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Yu. A. Klokov 《Differential Equations》2016,52(3):306-315
We obtain sufficient conditions for the existence of a solution of some boundary value problems for a fourth-order system. 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
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Using the bounding functions method and the theory of topological degree, this paper presents the existence criterion of solution for third-order BVP with nonlinear boundary conditions and extends the existing results. 相似文献
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A variational method is developed within the class of functions of boundary rotation not exceedingkπ which is based on the fact that the set of representing measuresμ is convex. It shows that an extremal problem related to a functional with Gateaux derivative and some constraints leads to
extremal measuresμ
0 with finite support. The positive and negative part of aμ
0 is located at points where a functionJ (depending onμ
0) reaches its maximum and minimum respectively. The method is tested successfully on various problems. 相似文献
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Boundary value problems for a new class of degenerate pseudodifferential equations containing a variable-symbol degenerate pseudodifferential operator based on a special integral transform and the first derivative with respect to one of the variables are studied. Existence theorems for these problems are proved. A priori estimates for their solutions are obtained in special weighted spaces similar to Sobolev ones. 相似文献
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Thordur Jonsson 《Journal of Differential Equations》1982,44(1):1-8
A procedure for investigating the global observability of a class of vectorfields is proposed. The method derives from given qualitative properties of the flow. It is shown that for Morse-Smale flows, local observability criteria can be tied together, leading to a global theorem. 相似文献
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Yulii A. Dubinskii 《Proceedings of the Steklov Institute of Mathematics》2016,293(1):151-160
Some nonstandard boundary value problems are studied for the stationary Poisson system, Stokes system, and Navier–Stokes system. The problems under consideration are “intermediate” between the Dirichlet problem and Neumann problem. The well-posedness of these problems is proved. 相似文献