共查询到20条相似文献,搜索用时 46 毫秒
1.
Antoine Lejay 《Probability Theory and Related Fields》2001,120(2):255-276
The probabilistic machinery (Central Limit Theorem, Feynman-Kac formula and Girsanov Theorem) is used to study the homogenization
property for PDE with second-order partial differential operator in divergence-form whose coefficients are stationary, ergodic
random fields. Furthermore, we use the theory of Dirichlet forms, so that the only conditions required on the coefficients
are non-degeneracy and boundedness.
Received: 27 August 1999 / Revised version: 27 October 2000 / Published online: 26 April 2001 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.
I. D. Berg 《Applicable analysis》2013,92(3):189-191
An elementary, intuitive proof is given of the theorem of HÖrmander that states that on a bounded domain in Rn the minimal operator corresponding to a differential polynomial with constant coefficients is 1-1 and of closed range. 相似文献
4.
David Colton 《Applicable analysis》2013,92(4):283-295
An integral operator is obtained which maps analytic functions of two complex variables onto solutions of a homogeneous linear elliptic partial differential equation in three independent variables. An inversion formula is given and used to construct a complete family of solutions for the elliptic equation under investigation 相似文献
5.
P. R. Popivanov 《Annali dell'Universita di Ferrara》2003,49(1):197-208
This paper deals with the local nonsolvability in Schwartz distribution spaceD′ ofm-order partial differential operator whose principal symbol is them-th power of locally solvable and hypoelliptic Mizohata type operator.
Sunto Questo lavoro tratta la nonrisolubilità locale nello spazio delle distribuzioni di SchwartzD′ degli operatori alle derivate parziali di ordinem il cui simbolo principale è lam-sima potenza dell'operatore tipo Mizohata localmente risolubile ed ipoellittico.相似文献
6.
V. L. Topunov 《Acta Appl Math》1989,16(2):191-206
In this paper, an application of the Riquer-Thomas-Janet theory is described for the problem of transforming a system of partial differential equations into a passive form, i.e., to a special form which contains explicitly both the equations of the initial system and all their nontrivial differential consequences. This special representation of a system markedly facilitates the subsequent integration of the corresponding differential equations. In this paper, the modern approach to the indicated problem is presented. This is the approach adopted in the Knuth-Bendix procedure [13] for critical-pair/completion and then Buchberger's algorithm for completion of polynomial ideal bases [13] (or, alternatively, for the construction of Groebner bases for ideals in a differential operator ring [14]). The algorithm of reduction to the passive form for linear system of partial differential equations and its implementation in the algorithmic language REFAL, as well as the capabilities of the corresponding program, are outlined. Examples illustrating the power and efficiency of the system are presented. 相似文献
7.
Yûsaku Hamada 《Journal of Fixed Point Theory and Applications》2007,1(2):209-220
In this article, we study analytic continuations of the solution of the Cauchy problem for a certain differential operator
in the complex domain.
à la mémoire de Jean Leray 相似文献
8.
We consider the heat operator acting on differential forms on spaces with complete and incomplete edge metrics. In the latter case we study the heat operator of the Hodge Laplacian with algebraic boundary conditions at the edge singularity. We establish the mapping properties of the heat operator, recovering and extending the classical results from smooth manifolds and conical spaces. The estimates, together with strong continuity of the heat operator, yield short‐time existence of solutions to certain semilinear parabolic equations. Our discussion reviews and generalizes earlier work by Jeffres and Loya. 相似文献
9.
The main goal of this paper is to prove existence and comparison results for elliptic differential inclusions governed by a quasilinear elliptic operator and a multivalued function given by Clarke’s generalized gradient of some locally Lipschitz function. These kinds of problems have been treated in the past by various authors including the authors of this paper. However, in all the works we are aware of, additional assumptions on the structure of the elliptic operator and/or the generalized Clarke’s gradient are needed to get comparison results in terms of sub-supersolutions. Comparison principles were obtained recently, e.g., in the case where the elliptic operator is of potential type, or Clarke’s gradient is required to satisfy some one-sided growth condition, or the sub-supersolutions are supposed to satisfy additional properties. The novelty of this paper is that we are able to obtain a comparison principle without assuming any of the above restrictions. To the best of our knowledge this is the first mathematical treatment of the considered elliptic inclusion in its full generality. The obtained results of this paper complement the development of the sub-supersolution method for nonsmooth problems presented in a recent monograph by S. Carl, Vy K. Le and D. Motreanu. 相似文献
10.
We study a class of optimization dynamics problems related to investment under uncertainty. The general model problem is
reformulated in terms of an obstacle problem associated to a second-order elliptic operator which is not in divergence form.
The spatial domain is unbounded and no boundary conditions are a priori specified. By using the special structure of the differential
operator and the spatial domain, and some approximating arguments, we show the existence and uniqueness of a solution of the
problem. We also study the regularity of the solution and give some estimates on the location of the coincidence set. 相似文献
11.
《Applied Mathematics and Optimization》2008,45(3):251-267
We study a class of optimization dynamics problems related to investment under uncertainty. The general model problem is
reformulated in terms of an obstacle problem associated to a second-order elliptic operator which is not in divergence form.
The spatial domain is unbounded and no boundary conditions are a priori specified. By using the special structure of the differential
operator and the spatial domain, and some approximating arguments, we show the existence and uniqueness of a solution of the
problem. We also study the regularity of the solution and give some estimates on the location of the coincidence set. 相似文献
12.
Parabolic initial boundary-value problems coupled (via the boundary condition) with ordinary differential equations whose right-hand side contains the Preisach hysteresis operator are considered. In particular, these problems model thermocontrol processes in chemical reactors, climate-control systems, biological cells, etc. For the Preisach operator with and without time delay, solvability, periodicity of solutions, and global B-attractors are studied. 相似文献
13.
A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations
We consider nonlinear elliptic equations driven by the p-Laplacian differential operator. Using degree theoretic arguments based on the degree map for operators of type (S)+ , we prove theorems on the existence of multiple nontrivial solutions of constant sign. 相似文献
14.
Vakhtang Lomadze 《Linear algebra and its applications》2011,435(11):2870-2888
A linear differential/integral operator is associated to a rational matrix in a natural way, and the behavior is defined to be the kernel of this operator. Conditions under which two rational matrices have the same behavior are derived. 相似文献
15.
Richard O. Moore 《Journal of Differential Equations》2008,245(6):1616-1655
We consider the semistrong limit of pulse interaction in a thermally driven, parametrically forced, nonlinear Schrödinger (TDNLS) system modeling pulse interaction in an optical cavity. The TDNLS couples a parabolic equation to a hyperbolic system, and in the semistrong scaling we construct pulse solutions which experience both short-range, tail-tail interactions and long-range thermal coupling. We extend the renormalization group (RG) methods used to derive semistrong interaction laws in reaction-diffusion systems to the hyperbolic-parabolic setting of the TDNLS system. A key step is to capture the singularly perturbed structure of the semigroup through the control of the commutator of the resolvent and a re-scaling operator. The RG approach reduces the pulse dynamics to a closed system of ordinary differential equations for the pulse locations. 相似文献
16.
Martin Väth 《Journal of Differential Equations》2008,245(5):1137-1166
The study of weak solutions for systems of nonlinear partial differential equations of elliptic type with inclusions leads to a multivalued operator of superposition type in Sobolev spaces. We show that, under natural assumptions, this operator has the properties which allow to apply degree theory (fixed point index) for multivalued maps. More precisely, this operator is upper semicontinuous and compact with nonempty convex compact values. For the particular case of systems involving p-Laplacians, we show that there is a homeomorphism transforming the whole system to a situation for which a fixed point index is available. 相似文献
17.
Michael E. Filippakis Nikolaos S. Papageorgiou Vasile Staicu 《Nonlinear Analysis: Theory, Methods & Applications》2008
In this paper we study eigenvalue problems for hemivariational and variational inequalities driven by the p-Laplacian differential operator. Using topological methods (based on multivalued versions of the Leray–Schauder alternative principle) and variational methods (based on the nonsmooth critical point theory), we prove existence and multiplicity results for the eigenvalue problems that we examine. 相似文献
18.
19.
Nikolaos S. Papageorgiou Eugénio M. Rocha Vasile Staicu 《Nonlinear Analysis: Theory, Methods & Applications》2008
We consider a parametric nonlinear elliptic inclusion with a multivalued p-Laplacian-like differential operator and a nonsmooth potential (hemivariational inequality). Using a variational approach based on the nonsmooth critical point theory, we show that for all the values of the parameter in an open half-line, the problem admits at least two nontrivial solutions. Our result extends a recent one by Kristály, Lisei, and Varga [A. Kristály, H. Lisei, C. Varga, Multiple solutions for p-Laplacian type operator, Nonlinear Anal. 68 (5) (2008) 1375–1381]. 相似文献
20.
We propose and test a new method for pricing American options in a high-dimensional setting. The method is centered around the approximation of the associated complementarity problem on an irregular grid. We approximate the partial differential operator on this grid by appealing to the SDE representation of the underlying process and computing the root of the transition probability matrix of an approximating Markov chain. Experimental results in five-dimensions are presented for four different payoff functions. 相似文献