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Yu. B. Zelinskii 《Ukrainian Mathematical Journal》1988,40(1):44-48
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 1, pp. 53–58, January–February, 1988. 相似文献
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The goal of this paper is to extend some maximum principles to the case of bounded convex domains with nonsmooth boundaries. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Let be a bounded, connected linearly convex set in with boundary. We show that the maximal ideal (both in ) and ) consisting of all functions vanishing at is generated by the coordinate functions .
Received: 2 July 2001; in final form: 26 September 2001 / Published online: 28 February 2002 相似文献
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E. L. Gurvitch 《Journal of Optimization Theory and Applications》1976,20(1):65-79
In the present paper, we discuss the isoperimetric problems for domains with partly known boundaries, i.e., the problem of determining a domain that minimizes the capacity functional in the class of plain double-connected domains having the same fixed area and outer boundary. The formulas for capacity variations obtained in this paper allows us to formulate necessary conditions.It is proved that the convexity of the fixed outer boundary implies the convexity of the inner boundary corresponding to an optimal domain. Then, we discuss the case where the fixed part of the boundary is a square.Further, we consider similar problems with more complicated functionals. We introduce the concept of a minimal function in the class of equimeasurable functions. This concept allows us to unify the approach to all of these problems. At the end, we produce a hypothesis that, if proved, would enable us to characterize the shape of the optimal domains in the isoperimetric problems mentioned above.The author wishes to express his appreciation to Dr. K. A. Lurie for his help and unceasing attention. 相似文献
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Sylvia Halász 《Journal of Combinatorial Theory, Series A》1984,37(1):85-90
Given a convex domain C and a positive integer k, inscribe k nonoverlapping convex domains into C, all of them similar to C. Denote by f(k) the maximal sum of their circumferences. In this paper it is shown, that for C square, parallelogram or triangle (1) the first increase of f(k) after k = l2 occurs not later than at k = l2 + 2, (2) constructions can be given, where the following lower bounds are attained for f(k) = f(l2 + j): where c denotes the circumference of C. 相似文献
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Rolf Schneider 《Journal of Geometry》1989,34(1-2):172-180
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Biholomorphic domains with inequivalent boundaries 总被引:1,自引:0,他引:1
David E. Barrett 《Inventiones Mathematicae》1986,85(2):373-377
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This paper is concerned with the analysis of a finite element method for nonhomogeneous second order elliptic interface problems on smooth domains. The method consists in approximating the domains by polygonal domains, transferring the boundary data in a natural way, and then applying a finite element method to the perturbed problem on the approximate polygonal domains. It is shown that the error in the finite element approximation is of optimal order for linear elements on a quasiuniform triangulation. As such the method is robust in the regularity of the data in the original problem. 相似文献
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Károly Bezdek 《Archiv der Mathematik》1992,58(6):611-614
The work was supported by Hung. Nat. Found. for Sci. Research No. 326-0213. 相似文献