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151.
We consider minimal energy configurations of mixtures of two materials in , where the energy includes a penalty on the length of the interface between the materials. We show that, for one of the materials,
the boundary of each component is smooth, and we prove the existence of an upper bound on the relative distances between components.
Received: 24 March 2000 / Accepted: 25 October 2001 / Published online: 29 April 2002 相似文献
152.
153.
We study regularity properties of quasiminimizers of the p-Dirichlet integral on metric measure spaces. We adapt the Moser iteration technique to this setting and show that it can be applied without an underlying differential equation. However, we have been able to run the Moser iteration fully only for minimizers. We prove Caccioppoli inequalities and local boundedness properties for quasisub- and quasisuperminimizers. This is done in metric spaces equipped with a doubling measure and supporting a weak (1, p)-Poincaré inequality. The metric space is not required to be complete. We also provide an example which shows that the dilation constant from the weak Poincaré inequality is essential in the condition on the balls in the Harnack inequality. This fact seems to have been overlooked in the earlier literature on nonlinear potential theory on metric spaces. 相似文献
154.
Sven Winklmann 《Archiv der Mathematik》2006,87(3):272-279
We give a new proof of Palmer’s result [6] that theWulff shapes are the only closed, oriented, stable hypersurfaces with constant
anisotropic mean curvature. Our approach is based on the construction of a suitable testfunction in the anisotropic index
form, thus generalizing the original proof of Barbosa, do Carmo [1].
Received: 3 August 2005 相似文献
155.
Stephan Luckhaus Thomas Sturzenhecker 《Calculus of Variations and Partial Differential Equations》1995,3(2):253-271
In this paper we apply the method of implicit time discretization to the mean curvature flow equation including outer forces. In the framework ofBV-functions we construct discrete solutions iteratively by minimizing a suitable energy-functional in each time step. Employing geometric and variational arguments we show an energy estimate which assures compactness of the discrete solutions. An additional convergence condition excludes a loss of area in the limit. Thus existence of solutions to the continuous problem can be derived. We append a brief discussion of the related Mullins-Sekerka equation.This work was supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 256, Bonn 相似文献
156.
In this paper we further develop the theory of the extended Timoshenko beam model, as first introduced in Part I [5] of this
work, with particular emphasis on applications of the model in formation theory [11], [12]. We begin with formal development
of the equilibrium equations of static formation theory in the context of the extended Timoshenko model, giving a rigorous
discussion of existence, uniqueness, and regularity of weak solutions with appropriate assumptions on the coefficients. We
continue to obtain the fundamental duality relationship in the context of weak solutions and indicate its usefulness in investigations
of approximate formability. Optimal formation problems and corresponding necessary conditions for optimality are discussed.
We conclude with a discussion of a particular problem of joint optimization of controls and actuator densities in the context
of a prismatic extended Timoshenko beam and we present the results of some computational studies.
Accepted 14 November 1996 相似文献
157.
Peter Kohlmann 《Geometriae Dedicata》1996,60(2):125-143
We consider noncompact, closed and convex sets with nonvoid interior in Euclidean space. It is shown that if such a set has one curvature measure sufficiently close to the boundary measure, then it is congruent to a product of a vector space and a compact convex body. Related stability and characterization theorems for orthogonal disc cylinders are proved. Our arguments are based on the Steiner-Schwarz symmetrization processes and generalized Minkowski integral formulas. 相似文献
158.
Friedrich Wehrung 《Algebra Universalis》2005,54(3):349-371
We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large.
As an application, we prove various results of which the following is a prototype: If every diagram, indexed by a lattice, of finite Boolean 〈∨ ,0 〉-semilattices with 〈∨ ,0 〉-embeddings, can be lifted, with respect to the Conc functor, by a diagram of lattices, then so can every diagram, indexed by a lattice, of finite distributive 〈∨ ,0 〉-semilattices with 〈∨ ,0 〉-embeddings. If the premise of this statement held, this would solve in turn the (still open) problem whether every distributive algebraic
lattice is isomorphic to the congruence lattice of a lattice. We also outline potential applications of our method to other
functors, such as the
functor on von Neumann regular rings.
Received August 12, 2004; accepted in final form June 6, 2005. 相似文献
159.
We consider the constrained vector optimization problem min C f(x), g(x) ∈ ?K, where f:? n →? m and g:? n →? p are C 1,1 functions, and C ? m and K ? p are closed convex cones with nonempty interiors. Two type of solutions are important for our considerations, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers). We formulate and prove in terms of the Dini directional derivative second-order necessary conditions for a point x 0 to be a w-minimizer and second-order sufficient conditions for x 0 to be an i-minimizer of order two. We discuss the reversal of the sufficient conditions under suitable constraint qualifications of Kuhn-Tucker type. The obtained results improve the ones in Liu, Neittaanmäki, K?í?ek [21]. 相似文献
160.
Let A be a self-adjoint operator in a Krein space
49_TeX2GIFIEq1.gif" alt="$(\mathcal{K},[ \cdot , \cdot ]).$
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Under certain natural assumptions, it is shown precisely which real eigenvalues of A can be given a max-inf characterization generalizing the usual one in Hilbert space. This result unifies several approaches in the recent literature. 相似文献