共查询到20条相似文献,搜索用时 31 毫秒
1.
Harmonic maps with potential 总被引:8,自引:0,他引:8
Ali Fardoun Andrea Ratto 《Calculus of Variations and Partial Differential Equations》1997,5(2):183-197
Let (M,g) and (N,h) be two Riemannian manifolds, and G:N →ℝ a given function. If f:M → N is a smooth map, we set E
G
(f)=12 ∫M [∣df∣2− 2G(f)]dv
g. We establish some variational properties and some existence results for the functional E
G
(f): in particular, we analyse the case of maps into a sphere.
Received April 29, 1996 / Accepted May 28, 1996 相似文献
2.
Bernard Dacorogna Irene Fonseca 《Calculus of Variations and Partial Differential Equations》2002,14(2):115-149
The study of existence of solutions of boundary-value problems for differential inclusions
where , is an open subset of , is a compact set, and B is a -valued first order differential operator, is undertaken. As an application, minima of the energy for large magnetic bodies
where the magnetization is taken with values on the unit sphere is the induced magnetic field satisfying and is the anisotropic energy density, and the applied external magnetic field is given by , are fully characterized. Setting with , it is shown that E admits a minimizer with if and only if either 0 is on a face of or , where denotes the convex hull of Z.
Received: 6 November 2000 / Accepted: 23 January 2001 / Published online: 23 April 2001 相似文献
3.
Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process
can be driven into a target set at a specified time. Differential properties of these sets are studied by the dynamic programming
principle which is proved by the Jankov-von Neumann measurable selection theorem. This principle implies that the reachability
sets satisfy a geometric partial differential equation, which is the analogue of the Hamilton-Jacobi-Bellman equation for
this problem. By appropriately choosing the controlled process, this connection provides a stochastic representation for mean
curvature type geometric flows. Another application is the super-replication problem in financial mathematics. Several applications
in this direction are also discussed.
Received October 24, 2000 / final version received July 24, 2001?Published online November 27, 2001 相似文献
4.
Luigi Ambrosio Nicola Fusco John E. Hutchinson 《Calculus of Variations and Partial Differential Equations》2003,16(2):187-215
The paper is concerned with the higher regularity properties of the minimizers of the Mumford–Shah functional. It is shown
that, near to singular points where the scaled Dirichlet integral tends to 0, the discontinuity set is close to an Almgren
area minimizing set. As a byproduct, the set of singular points of this type has Hausdorff dimension at most N-2, N being the dimension of the ambient space. Assuming higher integrability of the gradient this leads to an optimal estimate
of the Hausdorff dimension of the full singular set.
Received: 5 July 2001 / Accepted: 29 November 2001 / Published online: 23 May 2002 相似文献
5.
G. S. Weiss 《Calculus of Variations and Partial Differential Equations》2003,17(3):311-340
The equation where converges to the Dirac measure concentrated at with mass has been used as a model for the propagation of flames with high activation energy. For initial data that are bounded in
and have a uniformly bounded support, we study non-negative solutions of the Cauchy problem in as We show that each limit of is a solution of the free boundary problem in on (in the sense of domain variations and in a more precise sense). For a.e. time t the graph of u(t) has a unique tangent cone at -a.e. The free boundary is up to a set of vanishing measure the sum of a countably n-1-rectifiable set and of the set on which vanishes in the mean. The non-degenerate singular set is for a.e. time a countably n-1-rectifiable set. As key tools we introduce a monotonicity formula and, on the singular set, an estimate for the parabolic
mean frequency.
Received: 8 August 2001 / Accepted: 8 May 2002 / Published online: 5 September 2002
RID="a"
ID="a" Partially supported by a Grant-in-Aid for Scientific Research, Ministry of Education, Japan. 相似文献
6.
Martin Fuchs Gregory Seregin 《Calculus of Variations and Partial Differential Equations》1998,6(2):171-187
In the present paper we study regularity for local minimizers of the convex variational integral defined on certain classes of vector–valued functions . The underlying energy spaces are natural from the point of view of existence theory. We then show that local minimizers
are of class apart from a closed singular set with vanishing Lebesgue measure, provided . For twodimensional problems we obtain smoothness in the interior of .
Received June 21, 1996 / In revised form December 2, 1996 / Accepted December 17, 1996 相似文献
7.
Summary. In this paper, we present a convergence analysis applicable to the approximation of a large class of semi-coercive variational
inequalities. The approach we propose is based on a recession analysis of some regularized Galerkin schema. Finite-element
approximations of semi-coercive unilateral problems in mechanics are discussed. In particular, a Signorini-Fichera unilateral
contact model and some obstacle problem with frictions are studied. The theoretical conditions proved are in good agreement
with the numerical ones.
Received January 14, 1999 / Revised version received June 24, 1999 / Published online July 12, 2000 相似文献
8.
Robert E. Hartwig 《Linear and Multilinear Algebra》1981,10(1):59-61
A new criterion is given for rank additivity of a collection of m × n complex matrices. 相似文献
9.
Abstract. We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem
resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore
these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature. 相似文献
10.
《Applied Mathematics and Optimization》2008,47(1):27-44
Abstract. We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem
resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore
these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature. 相似文献
11.
In this paper, starting from the classical 3D non-convex and nonlocal micromagnetic energy for ferromagnetic materials, we determine, via an asymptotic analysis, the free energy of a multi-structure consisting of a nano-wire in junction with a thin film and of a multi-structure consisting of two joined nano-wires. We assume that the volumes of the two parts composing each multi-structure vanish with the same rate. In the first case, we obtain a 1D limit problem on the nano-wire and a 2D limit problem on the thin film, and the two limit problems are uncoupled. In the second case, we obtain two 1D limit problems coupled by a junction condition on the magnetization. In both cases, the limit problem remains non-convex, but now it becomes completely local. 相似文献
12.
Nabih N. Abdelmalek 《Numerical Functional Analysis & Optimization》2013,34(3-4):399-418
Two algorithms are here presented. The first one is for obtaining a Chebyshev solution of an overdetermined system of linear equations subject to bounds on the elements of the solution vector. The second algorithm is for obtaining an L1 solution of an overdetermined system of linear equations subject to the same constraints. Efficient solutions are obtained using linear programming techniques. Numerical results and comments are given. 相似文献
13.
Aleksandra Orpel 《Journal of Differential Equations》2004,204(1):247-264
We discuss the existence and the dependence on functional parameters of solutions of the Dirichlet problem for a kind of the generalization of the balance of a membrane equation. Since we shall propose an approach based on variational methods, we treat our equation as the Euler-Lagrange equation for a certain integral functional J. We will not impose either convexity or coercivity of the functional. We develop a duality theory which relates the infimum on a special set X of the energy functional associated with the problem, to the infimum of the dual functional on a corresponding set Xd. The links between minimizers of both functionals give a variational principle and, in consequence, their relation to our boundary value problem. We also present the numerical version of the variational principle. It enables the numerical characterization of approximate solutions and gives a measure of a duality gap between primal and dual functional for approximate solutions of our problem. 相似文献
14.
Lionel Thibault 《Journal of Differential Equations》2003,193(1):1-26
Differential inclusions involving the normal cone to a moving set are investigated. A special attention is paid to the sweeping process associated with sets for which no regularity assumption is required. 相似文献
15.
M.A. Sychev 《Calculus of Variations and Partial Differential Equations》2001,13(2):213-229
Given a compact set we consider the differential inclusion
We show how to use the main idea of the method of convex integration [ N], [G], [K] (to control convergence of the gradients of a sequence of approximate solutions by appropriate selection of the sequence)
to obtain an optimal existence result. We compare this result with the ones available by the Baire category approach applied
to the set of admissible functions with topology.
A byproduct of our result is attainment in the minimization problems
with integrands L having quasiaffine quasiconvexification that was, in fact, the reason of our interest to differential inclusions. This result
can be considered as a first step towards characterization of those minimization problems which are solvable for all boundary
data. This problem was solved in [S1] in the scalar case m=1.
Received November 5, 1998 / Accepted July 17, 2000 / Published online December 8, 2000 相似文献
16.
Alexander J. Zaslavski 《Calculus of Variations and Partial Differential Equations》2001,13(3):265-293
The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands
f which satisfy convexity and growth conditions. In [27] we considered a class of optimal control problems which is identified
with the corresponding complete metric space of integrands, say . We did not impose any convexity assumptions. The main result in [27] establishes that for a generic integrand the corresponding optimal control problem is well-posed. In this paper we study the set of all integrands for which the corresponding optimal control problem is well-posed. We show that the complement of this set is not only of
the first category but also a -porous set. The main result of the paper is obtained as a realization of a variational principle which can be applied to
various classes of optimization problems.
Received April 15, 2000 / Accepted October 10, 2000 / Published online December 8, 2000 相似文献
17.
Ciro D'Apice Umberto De Maio Peter I. Kogut 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2008
In this paper we study the asymptotic behaviour, as ε tends to zero, of a class of boundary optimal control problems Pε, set in ε-periodically perforated domain. The holes have a critical size with respect to ε -sized mesh of periodicity. The support of controls is contained in the set of boundaries of the holes. This set is divided into two parts, on one part the controls are of Dirichlet type; on the other one the controls are of Neumann type. We show that the optimal controls of the homogenized problem can be used as suboptimal ones for the problems Pε. 相似文献
18.
Adrian Tudorascu 《Calculus of Variations and Partial Differential Equations》2008,32(2):155-173
We prove the monotonicity of the second-order moments of the discrete approximations to the heat equation arising from the
Jordan–Kinderlehrer–Otto (JKO) variational scheme. This issue appears in the study of constrained optimization in the 2-Wasserstein
metric performed by Carlen and Gangbo for the kinetic Fokker–Planck equation. As an alternative to their duality method, we
provide the details of a direct approach, via Lagrange multipliers. Estimates for the fourth-order moments in the constrained
case, which are essential to the subsequent alternate analysis, are also obtained.
Partial support provided by NSF grant DMS 0305794. 相似文献
19.
Pietro Celada Stefania Perrotta 《Calculus of Variations and Partial Differential Equations》2001,12(4):371-398
We consider the problem of minimizing multiple integrals of product type, i.e.
where is a bounded, open set in , is a possibly nonconvex, lower semicontinuous function with p-growth at infinity for some and the boundary datum is in (or simply in if ). Assuming that the convex envelope off is affine on each connected component of the set , we prove attainment for () for every continuous, positively bounded below function g such that (i) every point is squeezed between two intervals where g is monotone and (ii) g has no strict local minima. This shows in particular that the class of coefficents g that yield existence to () is dense in the space of continuous, positive functions on . We present examples which show that these conditions for attainment are essentially sharp.
Received April 12, 2000 / Accepted May 9, 2000 / Published online November 9, 2000 相似文献
20.
J.Y. Bello Cruz 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2917-2922
We present a version of the projected gradient method for solving constrained minimization problems with a competitive search strategy: an appropriate step size rule through an Armijo search along the feasible direction, thereby obtaining global convergence properties when the objective function is quasiconvex or pseudoconvex. In contrast to other similar step size rules, this one requires only one projection onto the feasible set per iteration, rather than one projection for each tentative step during the search for the step size, which represents a considerable saving when the projections are computationally expensive. 相似文献