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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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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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We consider the Cauchy problem in Rn for strongly damped wave equations. We derive asymptotic profiles of these solutions with weighted L1,1(Rn) data by using a method introduced in [9] and/or [10]. 相似文献
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This paper is concerned with special regularity properties of the solutions to the Maxwell–Landau–Lifshitz (MLL) system describing ferromagnetic medium. Besides the classical results on the boundedness of ∂tm,∂tE and ∂tH in the spaces L∞(I,L2(Ω)) and L2(I,W1,2(Ω)) we derive also estimates in weighted Sobolev spaces. This kind of estimates can be used to control the Taylor remainder when estimating the error of a numerical scheme. 相似文献
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An exact finite-difference scheme for a system of two linear differential equations with constant coefficients, (d/dt)x(t)=Ax(t), is proposed. The scheme is different from what was proposed by Mickens [Nonstandard Finite Difference Models of Differential Equations, World Scientific, New Jersey, 1994, p. 147], in which the derivatives of the two equations are formed differently. Our exact scheme is in the form of (1/φ(h))(xk+1-xk)=A[θxk+1+(1-θ)xk]; both derivatives are in the same form of (xk+1-xk)/φ(h). 相似文献
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We study the existence of weak solutions to (E) (−Δ)αu+g(u)=ν in a bounded regular domain Ω in RN(N≥2) which vanish in RN?Ω, where (−Δ)α denotes the fractional Laplacian with α∈(0,1), ν is a Radon measure and g is a nondecreasing function satisfying some extra hypotheses. When g satisfies a subcritical integrability condition, we prove the existence and uniqueness of weak solution for problem (E) for any measure. In the case where ν is a Dirac measure, we characterize the asymptotic behavior of the solution. When g(r)=|r|k−1r with k supercritical, we show that a condition of absolute continuity of the measure with respect to some Bessel capacity is a necessary and sufficient condition in order (E) to be solved. 相似文献
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We study the existence of solutions u:R3→R2 for the semilinear elliptic systems where W:R2→R is a double well symmetric potential. We use variational methods to show, under generic non-degenerate properties of the set of one dimensional heteroclinic connections between the two minima a± of W, that (0.1) has infinitely many geometrically distinct solutions u∈C2(R3,R2) which satisfy u(x,y,z)→a± as x→±∞ uniformly with respect to (y,z)∈R2 and which exhibit dihedral symmetries with respect to the variables y and z . We also characterize the asymptotic behavior of these solutions as |(y,z)|→+∞. 相似文献
equation(0.1)
−Δu(x,y,z)+∇W(u(x,y,z))=0,
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We study a unilateral problem for the operator L perturbed of Navier–Stokes operator in a noncylindrical case, where
Here we considered a cylindrical domain and using an appropriate penalization, we obtained a variational inequality for the Navier–Stokes system. Here we transform the noncylindrical domain into a cylindrical domain using a diffeomorphism as in Vieira-Rabello Unilateral problem for the Navier–Stokes operators in noncylindrical domains, Comput. Appl. Math. 13(1) (1994) 67–79. 相似文献
Lu=u′-(ν0+ν1∥u(t)∥2)Δu+(u.∇)u-f+∇p.
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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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Under appropriate assumptions the higher order energy decay rates for the damped wave equations with variable coefficients c(x)utt−div(A(x)∇u)+a(x)ut=0 in Rn are established. The results concern weighted (in time) and pointwise (in time) energy decay estimates. We also obtain weighted L2 estimates for spatial derivatives. 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