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We calculate the Batalin–Vilkovisky, and the induced Gerstenhaber structures of the Hochschild cohomology of the singular R-cochain complex of n-dimensional K-projective spaces, where K=C,H and R=Z and any field. In the special case that K=C, n=1 and R=Z, we show that this structure cannot be identified with the BV-structure of the integral loop homology of the 2-dimensional sphere computed by L. Menichi, but their induced Gerstenhaber structures can still be identified. Combined with the work of Y. Félix and J. Thomas, the main result of the present paper calculates the BV-structure of the rational loop homology of projective spaces. 相似文献
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We consider the Penrose–Fife phase field model [Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D 43 (1990) 44–62] with homogeneous Neumann boundary condition to the nonlinear heat flux q=∇(1/θ), i.e., q=0 on the boundary, where θ>0 is the temperature. There is a unique H1 solution globally in time with the non-empty, connected, compact ω-limit set composed of stationary solutions, and the linearized stable stationary solution is dynamically stable. 相似文献
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Cristian Enache 《Comptes Rendus Mathematique》2014,352(1):37-42
In this note we derive a maximum principle for an appropriate functional combination of u(x) and |∇u|2, where u(x) is a strictly convex classical solution to a general class of Monge–Ampère equations. This maximum principle is then employed to establish some isoperimetric inequalities of interest in the theory of surfaces of constant Gauss curvature in RN+1. 相似文献
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We study the global existence of weak solutions to a multi-dimensional simplified Ericksen–Leslie system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain Ω⊂RN, where N=2 or 3. By exploiting a maximum principle, Nirenberg?s interpolation inequality and a smallness condition imposed on the N -th component of initial direction field d0 to overcome the difficulties induced by the supercritical nonlinearity |∇d|2d in the equations of angular momentum, and then adapting a modified three-dimensional approximation scheme and the weak convergence arguments for the compressible Navier–Stokes equations, we establish the global existence of weak solutions to the initial-boundary problem with large initial energy and without any smallness condition on the initial density and velocity. 相似文献
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We study a family of differential operators Lα in two variables, depending on the coupling parameter α?0 that appears only in the boundary conditions. Our main concern is the spectral properties of Lα, which turn out to be quite different for α<1 and for α>1. In particular, Lα has a unique self-adjoint realization for α<1 and many such realizations for α>1. In the more difficult case α>1 an analysis of non-elliptic pseudodifferential operators in dimension one is involved. 相似文献
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A basic geometric question is to determine when a given framework G(p) is globally rigid in Euclidean space Rd, where G is a finite graph and p is a configuration of points corresponding to the vertices of G . G(p) is globally rigid in Rd if for any other configuration q for G such that the edge lengths of G(q) are the same as the corresponding edge lengths of G(p), then p is congruent to q. A framework G(p) is redundantly rigid, if it is rigid and it remains rigid after the removal of any edge of G. 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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We study the large time behavior of solutions of the Cauchy problem for the Hamilton–Jacobi equation ut+H(x,Du)=0 in Rn×(0,∞), where H(x,p) is continuous on Rn×Rn and convex in p . We establish a general convergence result for viscosity solutions u(x,t) of the Cauchy problem as t→∞. 相似文献
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Time-discretization scheme for quasi-static Maxwell's equations with a non-linear boundary condition
We study a time dependent eddy current equation for the magnetic field H accompanied with a non-linear degenerate boundary condition (BC), which is a generalization of the classical Silver–Müller condition for a non-perfect conductor. More exactly, the relation between the normal components of electrical E and magnetic H fields obeys the following power law ν×E=ν×(|H×ν|α-1H×ν) for some α∈(0,1]. We establish the existence and uniqueness of a weak solution in a suitable function space under the minimal regularity assumptions on the boundary Γ and the initial data H0. We design a non-linear time discrete approximation scheme based on Rothe's method and prove convergence of the approximations to a weak solution. We also derive the error estimates for the time-discretization. 相似文献
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Francesco Altomare Mirella Cappelletti Montano Vita Leonessa Ioan Raşa 《Journal of Mathematical Analysis and Applications》2014
The paper is concerned with a special class of positive linear operators acting on the space C(K) of all continuous functions defined on a convex compact subset K of Rd, d?1, having non-empty interior. Actually, this class consists of all positive linear operators T on C(K) which leave invariant the polynomials of degree at most 1 and which, in addition, map polynomials into polynomials of the same degree. Among other things, we discuss the existence of such operators in the special case where K is strictly convex by also characterizing them within the class of positive projections. In particular we show that such operators exist if and only if ∂K is an ellipsoid. Furthermore, a characterization of balls of Rd in terms of a special class of them is furnished. Additional results and illustrative examples are presented as well. 相似文献
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Necessary and sufficient conditions of some strong optimal solutions to the interval linear programming 总被引:1,自引:0,他引:1
This paper considers optimal solutions of general interval linear programming problems. Necessary and sufficient conditions of (A,b)-strong and (A,b,c)-strong optimal solutions to the interval linear programming with inequality constraints are proposed. The features of the proposed methods are illustrated by some examples. 相似文献
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We study boundary value problems of the form -Δu=f on Ω and Bu=g on the boundary ∂Ω, with either Dirichlet or Neumann boundary conditions, where Ω is a smooth bounded domain in Rn and the data f,g are distributions . This problem has to be first properly reformulated and, for practical applications, it is of crucial importance to obtain the continuity of the solution u in terms of f and g . For f=0, taking advantage of the fact that u is harmonic on Ω, we provide four formulations of this boundary value problem (one using nontangential limits of harmonic functions, one using Green functions, one using the Dirichlet-to-Neumann map, and a variational one); we show that these four formulations are equivalent. We provide a similar analysis for f≠0 and discuss the roles of f and g, which turn to be somewhat interchangeable in the low regularity case. The weak formulation is more convenient for numerical approximation, whereas the nontangential limits definition is closer to the intuition and easier to check in concrete situations. We extend the weak formulation to polygonal domains using weighted Sobolev spaces. We also point out some new phenomena for the “concentrated loads” at the vertices in the polygonal case. 相似文献
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Crossing by lines all edges of a line arrangement 总被引:1,自引:0,他引:1