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1.
A comparison between some relaxation methods of an integral functional is carried out. The following relaxed functionals of the variational integral I(, u)= :
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2.
The fictitious domain method is applied to construct a difference scheme for the first boundary-value problem for elliptical equations of second order in domains of arbitrary shape. The rate of convergence bound
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3.
In this paper we consider the existence and asymptotic behavior of solutions of the following problem:
where q>1, q1, >0, >0, 0, is the Laplacian in .  相似文献   

4.
A unified theroy for the complementary-dual extremum energy theorems in nonlinear elastostatics is established under the global extremum criteria
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5.
In this paper we prove Lp () and -norm estimates for the solution of the elliptic equation:
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6.
An analog of the classical Fourier formula for the characteristic function of a convex compact set is considered:
where W is a polyhedral in . Bibliography: 6 titles.  相似文献   

7.
In this paper we prove the existence of at least one positive solution of the equation
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8.
We consider multi-dimensional variational integrals
where the integrand f is a strictly convex function of its last argument. We give an elementary proof for the partial -regularity of minimizers of F. Our approach is based on the method of A-harmonic approximation, avoids the use of Gehring’s lemma, and establishes partial regularity with the optimal H?lder exponent α in a single step.   相似文献   

9.
We study the existence of an integral representation for the functional
when μ is a positive Radon measure on ℝN, Ω⊂ℝN is a bounded open set, and is a continuous function not necessarily convex with growth conditions of order p>1. Mathematics Subject Classification (2000)  49J45, 49Q20  相似文献   

10.
Consider a plate occupying in a reference configuration a bounded open set Ω ⊂ ℝ 2 , and let be its stored-energy function. In this paper we are concerned with relaxation of variational problems of type:
, where with is the scalar product in ℝ 3 and is the external loading per unit surface. We take into account the fact that an infinite amount of energy is required to compress a finite surface of the plate into zero surface, i.e.,
Mathematics Subject Classification (2000) 49J45  相似文献   

11.
We prove the maximum principle for an optimal control problem governed by the system
with state constraint , under three different hypotheses: (H1) C is a convex set with nonempty interior; (H2) a convex set with nonempty interior in H and the evolution system satisfying compactness hypotheses; (H3) the periodic case , with the evolution system satisfying compactness hypotheses. We do not assume the controls to be bounded. We give some examples for distributed control problems.  相似文献   

12.
We consider the optimization of the two-dimensional transformation of the spatial arguments of the sought function in the mixed initial boundary-value problem for the functional-differential diffusion equation
where the right-hand side is defined by the generalized superposition , and the argument transformation g(x) in the form of the functional
defined on the space of continuous test functions . The quality of optimization is evaluated by the integral functional
The minimizing sequence for the minimization problem J(g) inf G on the set G = g L 2(Q): g ( ) } of pointwise-bounded transformations is constructed by the gradient projection method combined with special projection-difference approximations of the direct and the conjugate initial boundary-value problems, which allow for possible irreversibility of the argument transformation and its generalized specification. Numerical optimization results are discussed using two examples of localized objective functions u 1(x, t).  相似文献   

13.
We discuss the partial regularity of minimizers of energy functionals such as
where u is a map from a domain into the m-dimensional unit sphere of and A is a differential one-form in .  相似文献   

14.
We prove that theTrudinger-Moser constant
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15.
We study the existence and uniqueness of solutions of the convective–diffusive elliptic equation
posed in a bounded domain , with pure Neumann boundary conditions
Under the assumption that with p = N if N ≥ 3 (resp. p > 2 if N  =  2), we prove that the problem has a solution if ∫Ω f dx  = 0, and also that the kernel is generated by a function , unique up to a multiplicative constant, which satisfies a.e. on Ω. We also prove that the equation
has a unique solution for all ν > 0 and the map is an isomorphism of the respective spaces. The study is made in parallel with the dual problem, with equation
The dependence on the data is also examined, and we give applications to solutions of nonlinear elliptic PDE with measure data and to parabolic problems.  相似文献   

16.
Using the integral operator that defines a solution of the Cauchy problem for the equation
we find an integral representation for solutions of the equation
in terms of arbitrary functions that are continuously differentiable sufficiently many times.  相似文献   

17.
We solve Tikhomirov's problem on the explicit computation of sharp constants in the Kolmogorov type inequalities
Specifically, we prove that
for all and k{0,...,n-1}. We establish symmetry and regularity properties of the numbers A n,k and study their asymptotic behavior as n for the cases k=O(n 2/3) and k/n(0,1).Similar problems were previously studied by Gabushin and Taikov.  相似文献   

18.
The aim of this paper is investigating the existence of one or more critical points of a family of functionals which generalizes the model problem
in the Banach space , being Ω a bounded domain in . In order to use “classical” theorems, a suitable variant of condition (C) is proved and is decomposed according to a “good” sequence of finite dimensional subspaces. The authors acknowledge the support of M.I.U.R. (research funds ex 40% and 60%).  相似文献   

19.
The asymptotic behaviour of bounded solutions of evolutionary integral equations in a Banach spaceX
On the real line and of
On the half-line are studied. Assuming that the inhomogeneityf (resp.g) belongs to a given homogeneous subspace ofBUC(X) (resp.BUC( +;X)) it is shown that given bounded solutionsu (resp.v) belong also to provided the spectra of these equations are countable. The results are applied to an equation of scalar type which is of importance in applications like viscoelasticity.  相似文献   

20.
We consider the boundary-value problem
where and n is the unit outward normal. We show that there exist so many nonequivalent positive weak solutions as prescribed under certain conditions on q and R. We construct nonradial solutions for [(n + 1)/2] + 1 ⩽ p < n and some q. Bibliography: 18 titles.__________Translated from Problemy Matematicheskogo Analiza, No. 30, 2005, pp. 121–144.  相似文献   

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